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Simplifying 4x(x + -7) + 9(x + -7)(x + -7) = 0 Reorder the terms: 4x(-7 + x) + 9(x + -7)(x + -7) = 0 (-7 * 4x + x * 4x) + 9(x + -7)(x + -7) = 0 (-28x + 4x2) + 9(x + -7)(x + -7) = 0 Reorder the terms: -28x + 4x2 + 9(-7 + x)(x + -7) = 0 Reorder the terms: -28x + 4x2 + 9(-7 + x)(-7 + x) = 0 Multiply (-7 + x) * (-7 + x) -28x + 4x2 + 9(-7(-7 + x) + x(-7 + x)) = 0 -28x + 4x2 + 9((-7 * -7 + x * -7) + x(-7 + x)) = 0 -28x + 4x2 + 9((49 + -7x) + x(-7 + x)) = 0 -28x + 4x2 + 9(49 + -7x + (-7 * x + x * x)) = 0 -28x + 4x2 + 9(49 + -7x + (-7x + x2)) = 0 Combine like terms: -7x + -7x = -14x -28x + 4x2 + 9(49 + -14x + x2) = 0 -28x + 4x2 + (49 * 9 + -14x * 9 + x2 * 9) = 0 -28x + 4x2 + (441 + -126x + 9x2) = 0 Reorder the terms: 441 + -28x + -126x + 4x2 + 9x2 = 0 Combine like terms: -28x + -126x = -154x 441 + -154x + 4x2 + 9x2 = 0 Combine like terms: 4x2 + 9x2 = 13x2 441 + -154x + 13x2 = 0 Solving 441 + -154x + 13x2 = 0 Solving for variable 'x'. Factor a trinomial. (63 + -13x)(7 + -1x) = 0Subproblem 1
Set the factor '(63 + -13x)' equal to zero and attempt to solve: Simplifying 63 + -13x = 0 Solving 63 + -13x = 0 Move all terms containing x to the left, all other terms to the right. Add '-63' to each side of the equation. 63 + -63 + -13x = 0 + -63 Combine like terms: 63 + -63 = 0 0 + -13x = 0 + -63 -13x = 0 + -63 Combine like terms: 0 + -63 = -63 -13x = -63 Divide each side by '-13'. x = 4.846153846 Simplifying x = 4.846153846Subproblem 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 = {4.846153846, 7}
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