Question

Solving Quadratic Equations by Factoring Solve the following quadratic expressions by factoring. First write the expressions in completely factored form. Then write the real number solutions, [Hint: Remember to use proper notation when writing the real number solutions. For example: if the solutions are x = 1 and x = 4, write x = 1,4 x² + 11x = 30 Factored Form

Answer 1

To solve the quadratic equation x² + 11x = 30 by factoring, rearrange the equation to x² + 11x - 30 = 0. Find two numbers whose product is -30 and whose sum is 11, which are 6 and -5. The factored form of the expression is (x + 6)(x - 5) = 0. Solve each factor equal to zero to find the solutions, x = -6 and x = 5.

Step-by-step explanation:

To solve the quadratic equation x² + 11x = 30 by factoring, we first rearrange it to x² + 11x - 30 = 0. Then, we look for two numbers whose product is -30 and whose sum is 11. The numbers are 6 and -5. Therefore, the factored form of the expression is (x + 6)(x - 5) = 0. To find the solutions, we set each factor equal to zero and solve for x. So, x + 6 = 0 gives x = -6, and x - 5 = 0 gives x = 5.

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