![]() ![]() Step 5: Substitute either value (we'll use `+4`) into the `u` bracket expressions, giving us the same roots of the quadratic equation that we found above:įor more on this approach, see: A Different Way to Solve Quadratic Equations (video by Po-Shen Loh). Step 3: Set that expansion equal to the constant term: `1 - u^2 = -15` Step 1: Take −1/2 times the x coefficient. The following approach takes the guesswork out of the factoring step, and is similar to what we'll be doing next, in Completing the Square. We could have proceded as follows to solve this quadratic equation. (Similarly, when we substitute `x = -3`, we also get `0`.) Alternate method (Po-Shen Loh's approach) We check the roots in the original equation by Now, if either of the terms ( x − 5) or ( x + 3) is 0, the product is zero. (v) Check the solutions in the original equation (iv) Solve the resulting linear equations (i) Bring all terms to the left and simplify, leaving zero on Using the fact that a product is zero if any of its factors is zero we follow these steps: If you need a reminder on how to factor, go back to the section on: Factoring Trinomials. Solving a Quadratic Equation by Factoringįor the time being, we shall deal only with quadratic equations that can be factored (factorised). This can be seen by substituting x = 3 in the The quadratic equation x 2 − 6 x + 9 = 0 has double roots of x = 3 (both roots are the same) In this example, the roots are real and distinct. This can be seen by substituting in the equation: (We'll show below how to find these roots.) The quadratic equation x 2 − 7 x + 10 = 0 has roots of The solution of an equation consists of all numbers (roots) which make the equation true.Īll quadratic equations have 2 solutions (ie. x 3 − x 2 − 5 = 0 is NOT a quadratic equation because there is an x 3 term (not allowed in quadratic equations).bx − 6 = 0 is NOT a quadratic equation because there is no x 2 term.must NOT contain terms with degrees higher than x 2 eg.Solve a Quadratic Equation by COMPLETING THE SQUARE. To determine when the height of the ball is 336 feet. The distance along the ground from the bottom of the pole to the end of the wire is 4 feet greater than the height where the wire is attached to the pole. How far up the pole does the guy wire reach?Įxample 4: You throw a ball straight up from a rooftop 384 feet high with an initial speed of 3 feet per second. The functionĭescribes the height of the ball above the ground, s (t), in feet, t seconds after you threw it. The ball misses the rooftop on its way down and eventually strikes the ground. How long will it take for the ball to hit the ground? Eliminate any unreasonable answers.Įxample 2: Each side of a square is lengthened by 7 inches. The area of this new larger square is 81 square inches. Find the length of a side of the original square.Įxample 3: A guy wire is attached to a tree to help it grow straight. The length of the wire is 2 feet greater than the distance from the base of the tree to the stake. The height of the wooden part of the tree is 1 foot greater than the distance from the base of the tree to the stake.Įxample 5: A piece of wire measuring 20 feet is attached to a telephone pole as a guy wire. Step 6: Set each factor equal to 0. And solve the linear equation. Step 4: Write the equation in standard form. Substitute the given information to the equation. Step 3: Determine if there is a special formula needed. Step 1: Draw and label a picture if necessary. Įxample 1: A vacant rectangular lot is being turned into a community vegetable garden measuring 8 meters by 12 meters. A path of uniform width is to surround garden. If the area of the lot is 140 square meters, find the width of the path surrounding the garden. Solve a quadratic equation by using the Quadratic Formula. ![]() Solve a quadratic equation by completing the square. Learning Target 3: Solving by Non Factoring Methods Solve a quadratic equation by finding square roots. Create a quadratic equation given a graph or the zeros of a function. of carpet.)Īrea of a rectangle and Landscaping/border/frame problems. Solve a quadratic equation by factoring when a is not 1. Set each factor equal to 0. And solve the linear equation. Substitute the given information into the equation.Ħ. Determine if there is a special formula needed. Steps for solving Quadratic application problems:ġ. ![]()
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