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Simplifying 7x(x + -7) = (2x + 9)(x + -7) Reorder the terms: 7x(-7 + x) = (2x + 9)(x + -7) (-7 * 7x + x * 7x) = (2x + 9)(x + -7) (-49x + 7x2) = (2x + 9)(x + -7) Reorder the terms: -49x + 7x2 = (9 + 2x)(x + -7) Reorder the terms: -49x + 7x2 = (9 + 2x)(-7 + x) Multiply (9 + 2x) * (-7 + x) -49x + 7x2 = (9(-7 + x) + 2x * (-7 + x)) -49x + 7x2 = ((-7 * 9 + x * 9) + 2x * (-7 + x)) -49x + 7x2 = ((-63 + 9x) + 2x * (-7 + x)) -49x + 7x2 = (-63 + 9x + (-7 * 2x + x * 2x)) -49x + 7x2 = (-63 + 9x + (-14x + 2x2)) Combine like terms: 9x + -14x = -5x -49x + 7x2 = (-63 + -5x + 2x2) Solving -49x + 7x2 = -63 + -5x + 2x2 Solving for variable 'x'. Reorder the terms: 63 + -49x + 5x + 7x2 + -2x2 = -63 + -5x + 2x2 + 63 + 5x + -2x2 Combine like terms: -49x + 5x = -44x 63 + -44x + 7x2 + -2x2 = -63 + -5x + 2x2 + 63 + 5x + -2x2 Combine like terms: 7x2 + -2x2 = 5x2 63 + -44x + 5x2 = -63 + -5x + 2x2 + 63 + 5x + -2x2 Reorder the terms: 63 + -44x + 5x2 = -63 + 63 + -5x + 5x + 2x2 + -2x2 Combine like terms: -63 + 63 = 0 63 + -44x + 5x2 = 0 + -5x + 5x + 2x2 + -2x2 63 + -44x + 5x2 = -5x + 5x + 2x2 + -2x2 Combine like terms: -5x + 5x = 0 63 + -44x + 5x2 = 0 + 2x2 + -2x2 63 + -44x + 5x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 63 + -44x + 5x2 = 0 Factor a trinomial. (9 + -5x)(7 + -1x) = 0Subproblem 1
Set the factor '(9 + -5x)' equal to zero and attempt to solve: Simplifying 9 + -5x = 0 Solving 9 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -5x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -5x = 0 + -9 -5x = 0 + -9 Combine like terms: 0 + -9 = -9 -5x = -9 Divide each side by '-5'. x = 1.8 Simplifying x = 1.8Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {1.8, 7}
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