Solve the quadratic by factoring. 5x^(2)-24 x+12=2x+7 Answer: x=

Move Terms to One Side: First, we need to move all terms to one side of the equation to set it equal to zero. Subtract 2x and 7 from both sides of the equation. 5x^2 - 24x + 12 - 2x - 7 = 0 Combine like terms. 5x^2 - 26x + 5 = 0Factor the Quadratic Equation: Next, we need to factor the quadratic equation. We are looking for two numbers that multiply to 5 * 5 = 25 and add up to -26. The numbers that satisfy these conditions are -25 and -1.Write as Product of Binomials: Now we can write the quadratic as a product of two binomials using the numbers we found. 5x^2 - 26x + 5 = (5x - 1)(x - 5)Set Factors Equal to Zero: To find the solutions, we set each factor equal to zero and solve for x. First, set the first factor equal to zero: 5x - 1 = 0 Add 1 to both sides: 5x = 1 Divide by 5: x = 1/5Find Solutions: Now, set the second factor equal to zero: x - 5 = 0 Add 5 to both sides: x = 5

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Solve the quadratic by factoring.

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5 x^{2}-24 x+12=2 x+7

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Answer:

x=

Move Terms to One Side: First, we need to move all terms to one side of the equation to set it equal to zero. $\newline$ Subtract $2x$ and $7$ from both sides of the equation. $\newline$ $5x^2 - 24x + 12 - 2x - 7 = 0$ $\newline$ Combine like terms. $\newline$ $5x^2 - 26x + 5 = 0$
Factor the Quadratic Equation: Next, we need to factor the quadratic equation. We are looking for two numbers that multiply to $5 \times 5 = 25$ and add up to $-26$ . The numbers that satisfy these conditions are $-25$ and $-1$ .
Write as Product of Binomials: Now we can write the quadratic as a product of two binomials using the numbers we found. $5x^2 - 26x + 5 = (5x - 1)(x - 5)$
Set Factors Equal to Zero: To find the solutions, we set each factor equal to zero and solve for $x$ . First, set the first factor equal to zero: $5x - 1 = 0$ Add $1$ to both sides: $5x = 1$ Divide by $5$ : $x = \frac{1}{5}$
Find Solutions: Now, set the second factor equal to zero: $\newline$ $x - 5 = 0$ $\newline$ Add $5$ to both sides: $\newline$ $x = 5$