Solve for all values of x by factoring. x^(2)+x-10=x-1 Answer: x=

Set Equation to Zero: Write down the given equation and move all terms to one side to set the equation to zero. x^2 + x - 10 = x - 1 Subtract x from both sides and add 1 to both sides to get: x^2 + x - x - 10 - 1 = 0 Simplify the equation: x^2 - 10 + 1 = 0 x^2 - 9 = 0Factor Quadratic Equation: Factor the quadratic equation. We need to find two numbers that multiply to -9 and add up to 0. The numbers that satisfy these conditions are 3 and -3. So, we can factor the equation as: (x + 3)(x - 3) = 0Use Zero Product Property: Use the zero product property to find the values of x. If (x + 3)(x - 3) = 0, then either x + 3 = 0 or x - 3 = 0. Solve for x in each case: x + 3 = 0 gives x = -3 x - 3 = 0 gives x = 3

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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-10=x-1

\newline

Answer:

x=

Set Equation to Zero: Write down the given equation and move all terms to one side to set the equation to zero. $\newline$ $x^2 + x - 10 = x - 1$ $\newline$ Subtract $x$ from both sides and add $1$ to both sides to get: $\newline$ $x^2 + x - x - 10 - 1 = 0$ $\newline$ Simplify the equation: $\newline$ $x^2 - 10 + 1 = 0$ $\newline$ $x^2 - 9 = 0$
Factor Quadratic Equation: Factor the quadratic equation. $\newline$ We need to find two numbers that multiply to $-9$ and add up to $0$ . The numbers that satisfy these conditions are $3$ and $-3$ . $\newline$ So, we can factor the equation as: $\newline$ $(x + 3)(x - 3) = 0$
Use Zero Product Property: Use the zero product property to find the values of $x$ . If $(x + 3)(x - 3) = 0$ , then either $x + 3 = 0$ or $x - 3 = 0$ . Solve for $x$ in each case: $x + 3 = 0$ gives $x = -3$ $x - 3 = 0$ gives $x = 3$