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

Set Standard Form: First, we need to set the quadratic equation to the standard form ax^2 + bx + c = 0 by moving all terms to one side of the equation. x^2 + 5 = 11x - 5 x^2 - 11x + 5 + 5 = 0 x^2 - 11x + 10 = 0Factor Quadratic Expression: Now, we need to factor the quadratic expression x^2 - 11x + 10. We are looking for two numbers that multiply to 10 (the constant term) and add up to -11 (the coefficient of x). The numbers that satisfy these conditions are -10 and -1 because: -10 * -1 = 10 -10 + -1 = -11Write Factored Form: We can now write the factored form of the quadratic equation using the numbers we found: x^2 - 11x + 10 = (x - 10)(x - 1)Find Solutions: To find the solutions to the equation, we set each factor equal to zero and solve for x: x - 10 = 0 or x - 1 = 0 x = 10 or x = 1

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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}+5=11 x-5

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Answer:

x=

Set Standard Form: First, we need to set the quadratic equation to the standard form $ax^2 + bx + c = 0$ by moving all terms to one side of the equation. $\newline$ $x^2 + 5 = 11x - 5$ $\newline$ $x^2 - 11x + 5 + 5 = 0$ $\newline$ $x^2 - 11x + 10 = 0$
Factor Quadratic Expression: Now, we need to factor the quadratic expression $x^2 - 11x + 10$ . We are looking for two numbers that multiply to $10$ (the constant term) and add up to $-11$ (the coefficient of $x$ ). The numbers that satisfy these conditions are $-10$ and $-1$ because: $-10 \times -1 = 10$ $-10 + -1 = -11$
Write Factored Form: We can now write the factored form of the quadratic equation using the numbers we found: $x^2 - 11x + 10 = (x - 10)(x - 1)$
Find Solutions: To find the solutions to the equation, we set each factor equal to zero and solve for $x$ : $x - 10 = 0$ or $x - 1 = 0$ $x = 10$ or $x = 1$