Consider \(x=20\) miles per hour to be the only solution.\(\require\) The latter will involve solving a quadratic equation, which will call for your newly acquired solving-by-factoring skills. To solve a quadratic equation in its factored form, we set each factor equal to 0 and then solve the resulting linear equations. Possibly a Binomial Square, which has the form: a2 + 2ab + b2 (a + b)2. 1 2(4) 2 22 4 Add (1 2)2 to both sides of the equal sign and simplify the right side. Since both terms are perfect squares, factor using the difference of squares formula, a2b2(a+b)(ab) a 2 - b 2 ( a + b ) ( a - b ) where ax a x and b1. However, we can use a technique called completing the square to rewrite the quadratic expression as a perfect square trinomial. Given a quadratic equation that cannot be factored, and with a 1, first add or subtract the constant term to the right sign of the equal sign. x2 + 4x + 1 0 x2 + 4x 1 Multiply the b term by 1 2 and square it. There are three main ways to solve quadratic equations: 1) to factor the quadratic equation if you can do so, 2) to use the quadratic formula, or 3) to complete. Transform the equation using standard form in which one side is zero. Factor trinomials (3 terms) using trial and error or the AC method. Given a quadratic equation that cannot be factored, and with a 1, first add or subtract the constant term to the right sign of the equal sign. Sometimes they are the same solution and the equation degrades to a single solution. To solve an quadratic equation using factoring : 1 1. Factor four-term polynomials by grouping (either GCF of pairs, or binomial square then difference of squares). Summary You can find the solutions, or roots, of quadratic equations by setting one side equal to zero, factoring the polynomial, and then applying the Zero Product Property. Step 2: Determine the number of terms in the polynomial. It discusses how to factor the gcf - greatest common factor, trin. The negative answer does not make sense in the context of this problem. In this last video example, we solve a quadratic equation with a leading coefficient of -1 using a shortcut method of factoring and the zero product principle. This algebra introduction tutorial explains how to solve quadratic equations by factoring.
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