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Simplifying 20 = 15x(8x + -12) Reorder the terms: 20 = 15x(-12 + 8x) 20 = (-12 * 15x + 8x * 15x) 20 = (-180x + 120x2) Solving 20 = -180x + 120x2 Solving for variable 'x'. Reorder the terms: 20 + 180x + -120x2 = -180x + 180x + 120x2 + -120x2 Combine like terms: -180x + 180x = 0 20 + 180x + -120x2 = 0 + 120x2 + -120x2 20 + 180x + -120x2 = 120x2 + -120x2 Combine like terms: 120x2 + -120x2 = 0 20 + 180x + -120x2 = 0 Factor out the Greatest Common Factor (GCF), '20'. 20(1 + 9x + -6x2) = 0 Ignore the factor 20.Subproblem 1
Set the factor '(1 + 9x + -6x2)' equal to zero and attempt to solve: Simplifying 1 + 9x + -6x2 = 0 Solving 1 + 9x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -0.1666666667 + -1.5x + x2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + -1.5x + 0.1666666667 + x2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + -1.5x + x2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + -1.5x + x2 = 0 + 0.1666666667 -1.5x + x2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 -1.5x + x2 = 0.1666666667 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 0.1666666667 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 0.1666666667 + 0.5625 Combine like terms: 0.1666666667 + 0.5625 = 0.7291666667 0.5625 + -1.5x + x2 = 0.7291666667 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 0.7291666667 Calculate the square root of the right side: 0.853912564 Break this problem into two subproblems by setting (x + -0.75) equal to 0.853912564 and -0.853912564.Subproblem 1
x + -0.75 = 0.853912564 Simplifying x + -0.75 = 0.853912564 Reorder the terms: -0.75 + x = 0.853912564 Solving -0.75 + x = 0.853912564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 0.853912564 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 0.853912564 + 0.75 x = 0.853912564 + 0.75 Combine like terms: 0.853912564 + 0.75 = 1.603912564 x = 1.603912564 Simplifying x = 1.603912564Subproblem 2
x + -0.75 = -0.853912564 Simplifying x + -0.75 = -0.853912564 Reorder the terms: -0.75 + x = -0.853912564 Solving -0.75 + x = -0.853912564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -0.853912564 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -0.853912564 + 0.75 x = -0.853912564 + 0.75 Combine like terms: -0.853912564 + 0.75 = -0.103912564 x = -0.103912564 Simplifying x = -0.103912564Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.603912564, -0.103912564}Solution
x = {1.603912564, -0.103912564}
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