Solve for all values of x by factoring. x^(2)+x+5=5 Answer: x=

Simplify Equation: Simplify the equation by subtracting 5 from both sides to set the equation to zero. x^2 + x + 5 - 5 = 5 - 5 x^2 + x = 0Factor Simplified Equation: Factor the simplified equation. The equation x^2 + x = 0 can be factored by taking x common. x(x + 1) = 0Apply Zero-Product Property: Apply the zero-product property. 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 = 0 or x + 1 = 0Solve for x: Solve each equation for x. For the first factor: x = 0 For the second factor: x + 1 = 0 x = -1

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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}+x+5=5

\newline

Answer:

x=

Simplify Equation: Simplify the equation by subtracting $5$ from both sides to set the equation to zero. $\newline$ $x^2 + x + 5 - 5 = 5 - 5$ $\newline$ $x^2 + x = 0$
Factor Simplified Equation: Factor the simplified equation. $\newline$ The equation $x^2 + x = 0$ can be factored by taking $x$ common. $\newline$ $x(x + 1) = 0$
Apply Zero-Product Property: Apply the zero-product property. $\newline$ 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 $x$ . $\newline$ $x = 0$ or $x + 1 = 0$
Solve for x: Solve each equation for x. $\newline$ For the first factor: $\newline$ $x = 0$ $\newline$ For the second factor: $\newline$ $x + 1 = 0$ $\newline$ $x = -1$