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Simplifying 4x + 8x + 80 = 6x2 + -4x Reorder the terms: 80 + 4x + 8x = 6x2 + -4x Combine like terms: 4x + 8x = 12x 80 + 12x = 6x2 + -4x Reorder the terms: 80 + 12x = -4x + 6x2 Solving 80 + 12x = -4x + 6x2 Solving for variable 'x'. Combine like terms: 12x + 4x = 16x 80 + 16x + -6x2 = -4x + 6x2 + 4x + -6x2 Reorder the terms: 80 + 16x + -6x2 = -4x + 4x + 6x2 + -6x2 Combine like terms: -4x + 4x = 0 80 + 16x + -6x2 = 0 + 6x2 + -6x2 80 + 16x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 80 + 16x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(40 + 8x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(40 + 8x + -3x2)' equal to zero and attempt to solve: Simplifying 40 + 8x + -3x2 = 0 Solving 40 + 8x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -13.33333333 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '13.33333333' to each side of the equation. -13.33333333 + -2.666666667x + 13.33333333 + x2 = 0 + 13.33333333 Reorder the terms: -13.33333333 + 13.33333333 + -2.666666667x + x2 = 0 + 13.33333333 Combine like terms: -13.33333333 + 13.33333333 = 0.00000000 0.00000000 + -2.666666667x + x2 = 0 + 13.33333333 -2.666666667x + x2 = 0 + 13.33333333 Combine like terms: 0 + 13.33333333 = 13.33333333 -2.666666667x + x2 = 13.33333333 The x term is -2.666666667x. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667x + 1.777777780 + x2 = 13.33333333 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 13.33333333 + 1.777777780 Combine like terms: 13.33333333 + 1.777777780 = 15.11111111 1.777777780 + -2.666666667x + x2 = 15.11111111 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 15.11111111 Calculate the square root of the right side: 3.887301263 Break this problem into two subproblems by setting (x + -1.333333334) equal to 3.887301263 and -3.887301263.Subproblem 1
x + -1.333333334 = 3.887301263 Simplifying x + -1.333333334 = 3.887301263 Reorder the terms: -1.333333334 + x = 3.887301263 Solving -1.333333334 + x = 3.887301263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = 3.887301263 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 3.887301263 + 1.333333334 x = 3.887301263 + 1.333333334 Combine like terms: 3.887301263 + 1.333333334 = 5.220634597 x = 5.220634597 Simplifying x = 5.220634597Subproblem 2
x + -1.333333334 = -3.887301263 Simplifying x + -1.333333334 = -3.887301263 Reorder the terms: -1.333333334 + x = -3.887301263 Solving -1.333333334 + x = -3.887301263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = -3.887301263 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -3.887301263 + 1.333333334 x = -3.887301263 + 1.333333334 Combine like terms: -3.887301263 + 1.333333334 = -2.553967929 x = -2.553967929 Simplifying x = -2.553967929Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.220634597, -2.553967929}Solution
x = {5.220634597, -2.553967929}
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