Solve for all values of x by factoring. x^(2)+10 x-4=x-4 Answer: x=

Write Equation and Simplify: Write down the given equation and simplify it by moving all terms to one side. x^2 + 10x - 4 = x - 4 Subtract x from both sides and add 4 to both sides to get: x^2 + 9x = 0Factor Simplified Equation: Factor the simplified equation. We can factor out an x from the left side of the equation: x(x + 9) = 0Apply Zero Product Property: Apply the zero product property. If the product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero and solve for x: x = 0 or x + 9 = 0Solve for x: Solve each equation for x. For the first factor: x = 0 For the second factor: x + 9 = 0 Subtract 9 from both sides: x = -9

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Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

Full solution

Q. Solve for all values of

x

by factoring.

\newline

x^{2}+10 x-4=x-4

\newline

Answer:

x=

Write Equation and Simplify: Write down the given equation and simplify it by moving all terms to one side. $\newline$ $x^2 + 10x - 4 = x - 4$ $\newline$ Subtract $x$ from both sides and add $4$ to both sides to get: $\newline$ $x^2 + 9x = 0$
Factor Simplified Equation: Factor the simplified equation. $\newline$ We can factor out an $x$ from the left side of the equation: $\newline$ $x(x + 9) = 0$
Apply Zero Product Property: Apply the zero product property. $\newline$ If the product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero and solve for $x$ : $\newline$ $x = 0$ or $x + 9 = 0$
Solve for x: Solve each equation for x. $\newline$ For the first factor: $\newline$ $x = 0$ $\newline$ For the second factor: $\newline$ $x + 9 = 0$ $\newline$ Subtract $9$ from both sides: $\newline$ $x = -9$