Solve the quadratic by factoring. x^(2)+11=5x+5 Answer: x=

Write Standard Form: Write the quadratic equation in standard form. To solve the quadratic equation by factoring, we need to write it in the form ax^2 + bx + c = 0. We start by subtracting 5x + 5 from both sides of the equation x^2 + 11 = 5x + 5. Calculation: x^2 + 11 - 5x - 5 = 0 Simplification: x^2 - 5x + 6 = 0Factor Quadratic Expression: Factor the quadratic expression. We need to find two numbers that multiply to give the constant term (c = 6) and add to give the coefficient of the x term (b = -5). The numbers that satisfy these conditions are -2 and -3. Calculation: (x - 2)(x - 3) = 0Solve Using Zero Product Property: Solve for x using the zero product property. If the product of two factors is zero, then at least one of the factors must be zero. We set each factor equal to zero and solve for x. Calculation: x - 2 = 0 or x - 3 = 0 x = 2 or x = 3

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Algebra 1

Factor quadratics with leading coefficient 1

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Q. Solve the quadratic by factoring.

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x^{2}+11=5 x+5

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Answer:

x=

Write Standard Form: Write the quadratic equation in standard form. $\newline$ To solve the quadratic equation by factoring, we need to write it in the form $ax^2 + bx + c = 0$ . We start by subtracting $5x + 5$ from both sides of the equation $x^2 + 11 = 5x + 5$ . $\newline$ Calculation: $x^2 + 11 - 5x - 5 = 0$ $\newline$ Simplification: $x^2 - 5x + 6 = 0$
Factor Quadratic Expression: Factor the quadratic expression. $\newline$ We need to find two numbers that multiply to give the constant term $c = 6$ and add to give the coefficient of the $x$ term $b = -5$ . $\newline$ The numbers that satisfy these conditions are $-2$ and $-3$ . $\newline$ Calculation: $(x - 2)(x - 3) = 0$
Solve Using Zero Product Property: Solve for $x$ using the zero product property. $\newline$ If the product of two factors is zero, then at least one of the factors must be zero. We set each factor equal to zero and solve for $x$ . $\newline$ Calculation: $\newline$ $x - 2 = 0$ or $x - 3 = 0$ $\newline$ $x = 2$ or $x = 3$