Solve the quadratic by factoring. x^(2)+x-56=-x+7 Answer: x=

Move Terms, Combine Like Terms: First, we need to move all terms to one side of the equation to set it equal to zero. x^2 + x - 56 + x - 7 = 0 Combine like terms. x^2 + 2x - 63 = 0Factor Quadratic Equation: Now, we need to factor the quadratic equation x^2 + 2x - 63. We are looking for two numbers that multiply to -63 and add up to 2. The numbers 9 and -7 work because 9 * -7 = -63 and 9 + (-7) = 2. So, we can write the factored form as (x + 9)(x - 7) = 0.Apply Zero Product Property: Next, we apply the zero product property, which states that if a product of two factors is zero, then at least one of the factors must be zero. So, we set each factor equal to zero and solve for x. x + 9 = 0 or x - 7 = 0Solve for x in First Equation: Solving the first equation x + 9 = 0 for x gives us: x = -9Solve for x in Second Equation: Solving the second equation x - 7 = 0 for x gives us: x = 7

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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}+x-56=-x+7

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Answer:

x=

Move Terms, Combine Like Terms: First, we need to move all terms to one side of the equation to set it equal to zero. $\newline$ $x^2 + x - 56 + x - 7 = 0$ $\newline$ Combine like terms. $\newline$ $x^2 + 2x - 63 = 0$
Factor Quadratic Equation: Now, we need to factor the quadratic equation $x^2 + 2x - 63$ . We are looking for two numbers that multiply to $-63$ and add up to $2$ . The numbers $9$ and $-7$ work because $9 \times -7 = -63$ and $9 + (-7) = 2$ . So, we can write the factored form as $(x + 9)(x - 7) = 0$ .
Apply Zero Product Property: Next, we apply the zero product property, which states that if a product of two factors is zero, then at least one of the factors must be zero. $\newline$ So, we set each factor equal to zero and solve for $x$ . $\newline$ $x + 9 = 0$ or $x - 7 = 0$
Solve for x in First Equation: Solving the first equation $x + 9 = 0$ for $x$ gives us: $\newline$ $x = -9$
Solve for x in Second Equation: Solving the second equation $x - 7 = 0$ for $x$ gives us: $x = 7$