Solve the quadratic by factoring. x^(2)-9=-x-7 Answer: x=

Write Standard Form: Write the quadratic equation in standard form. To solve the quadratic equation by factoring, we need to write it in the standard form ax^2 + bx + c = 0. We start by adding x and 7 to both sides of the equation x^2 - 9 = -x - 7. Calculation: x^2 + x - 9 + 7 = 0 x^2 + x - 2 = 0Factor Quadratic Expression: Factor the quadratic expression. We need to find two numbers that multiply to -2 (the constant term) and add up to 1 (the coefficient of x). The numbers that satisfy these conditions are 2 and -1. Calculation: (x + 2)(x - 1) = 0Solve for x: Solve for x using the zero product property. If the product of two factors is zero, then at least one of the factors must be zero. We set each factor equal to zero and solve for x. Calculation: x + 2 = 0 or x - 1 = 0 x = -2 or x = 1

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Algebra 1

Factor quadratics with leading coefficient 1

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Q. Solve the quadratic by factoring.

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x^{2}-9=-x-7

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Answer:

x=

Write Standard Form: Write the quadratic equation in standard form. $\newline$ To solve the quadratic equation by factoring, we need to write it in the standard form $ax^2 + bx + c = 0$ . We start by adding $x$ and $7$ to both sides of the equation $x^2 - 9 = -x - 7$ . $\newline$ Calculation: $x^2 + x - 9 + 7 = 0$ $\newline$ $x^2 + x - 2 = 0$
Factor Quadratic Expression: Factor the quadratic expression. $\newline$ We need to find two numbers that multiply to $-2$ (the constant term) and add up to $1$ (the coefficient of $x$ ). The numbers that satisfy these conditions are $2$ and $-1$ . $\newline$ Calculation: $(x + 2)(x - 1) = 0$
Solve for x: Solve for x using the zero product property. $\newline$ If the product of two factors is zero, then at least one of the factors must be zero. We set each factor equal to zero and solve for x. $\newline$ Calculation: $x + 2 = 0$ or $x - 1 = 0$ $\newline$ $x = -2$ or $x = 1$