Solve the quadratic by factoring. x^(2)+3x-30=10 Answer: x=

Set Quadratic Equation to Zero: First, we need to set the quadratic equation to zero by subtracting 10 from both sides of the equation. x^2 + 3x - 30 - 10 = 0 Simplify the equation. x^2 + 3x - 40 = 0Factor Quadratic Equation: Now, we need to factor the quadratic equation x^2 + 3x - 40. We are looking for two numbers that multiply to -40 and add up to 3. The numbers 8 and -5 satisfy these conditions because 8 * (-5) = -40 and 8 + (-5) = 3.Write Factored Form: Write the factored form of the quadratic equation using the numbers 8 and -5. (x + 8)(x - 5) = 0Solve for x (Factor 1): Now, we will solve for x by setting each factor equal to zero. First, set the first factor equal to zero: x + 8 = 0 Solve for x: x = -8Solve for x (Factor 2): Next, set the second factor equal to zero: x - 5 = 0 Solve for x: x = 5

Home

Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

Full solution

Q. Solve the quadratic by factoring.

\newline

x^{2}+3 x-30=10

\newline

Answer:

x=

Set Quadratic Equation to Zero: First, we need to set the quadratic equation to zero by subtracting $10$ from both sides of the equation. $\newline$ $x^2 + 3x - 30 - 10 = 0$ $\newline$ Simplify the equation. $\newline$ $x^2 + 3x - 40 = 0$
Factor Quadratic Equation: Now, we need to factor the quadratic equation $x^2 + 3x - 40$ . We are looking for two numbers that multiply to $-40$ and add up to $3$ . The numbers $8$ and $-5$ satisfy these conditions because $8 \times (-5) = -40$ and $8 + (-5) = 3$ .
Write Factored Form: Write the factored form of the quadratic equation using the numbers $8$ and $-5$ . $(x + 8)(x - 5) = 0$
Solve for x (Factor $1$ ): Now, we will solve for x by setting each factor equal to zero. $\newline$ First, set the first factor equal to zero: $\newline$ $x + 8 = 0$ $\newline$ Solve for x: $\newline$ $x = -8$
Solve for x (Factor $2$ ): Next, set the second factor equal to zero: $\newline$ $x - 5 = 0$ $\newline$ Solve for x: $\newline$ $x = 5$