Solve the quadratic by factoring. x^(2)+14 x+46=-x-8 Answer: x=

Move to Standard Form: Write the equation in standard form by moving all terms to one side. x^2 + 14x + 46 = -x - 8 Add x to both sides and add 8 to both sides to get: x^2 + 14x + x + 46 + 8 = 0 Combine like terms: x^2 + 15x + 54 = 0Factor Quadratic Equation: Factor the quadratic equation. We need to find two numbers that multiply to 54 (the constant term) and add up to 15 (the coefficient of the x term). The numbers 6 and 9 satisfy these conditions because: 6 * 9 = 54 6 + 9 = 15 So we can factor the quadratic as: (x + 6)(x + 9) = 0Solve for x: Solve for x by setting each factor equal to zero. x + 6 = 0 or x + 9 = 0 Solve each equation for x: x = -6 or x = -9

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Algebra 1

Factor quadratics with leading coefficient 1

Full solution

Q. Solve the quadratic by factoring.

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x^{2}+14 x+46=-x-8

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Answer:

x=

Move to Standard Form: Write the equation in standard form by moving all terms to one side. $\newline$ $x^2 + 14x + 46 = -x - 8$ $\newline$ Add $x$ to both sides and add $8$ to both sides to get: $\newline$ $x^2 + 14x + x + 46 + 8 = 0$ $\newline$ Combine like terms: $\newline$ $x^2 + 15x + 54 = 0$
Factor Quadratic Equation: Factor the quadratic equation. $\newline$ We need to find two numbers that multiply to $54$ (the constant term) and add up to $15$ (the coefficient of the $x$ term). $\newline$ The numbers $6$ and $9$ satisfy these conditions because: $\newline$ $6 \times 9 = 54$ $\newline$ $6 + 9 = 15$ $\newline$ So we can factor the quadratic as: $\newline$ $(x + 6)(x + 9) = 0$
Solve for x: Solve for x by setting each factor equal to zero. $\newline$ $x + 6 = 0$ or $x + 9 = 0$ $\newline$ Solve each equation for x: $\newline$ $x = -6$ or $x = -9$