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Simplifying -16x2 + 32x + 12 = 0 Reorder the terms: 12 + 32x + -16x2 = 0 Solving 12 + 32x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(3 + 8x + -4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3 + 8x + -4x2)' equal to zero and attempt to solve: Simplifying 3 + 8x + -4x2 = 0 Solving 3 + 8x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.75 + -2x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -2x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -2x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -2x + x2 = 0 + 0.75 -2x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -2x + x2 = 0.75 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 0.75 + 1 Reorder the terms: 1 + -2x + x2 = 0.75 + 1 Combine like terms: 0.75 + 1 = 1.75 1 + -2x + x2 = 1.75 Factor a perfect square on the left side: (x + -1)(x + -1) = 1.75 Calculate the square root of the right side: 1.322875656 Break this problem into two subproblems by setting (x + -1) equal to 1.322875656 and -1.322875656.Subproblem 1
x + -1 = 1.322875656 Simplifying x + -1 = 1.322875656 Reorder the terms: -1 + x = 1.322875656 Solving -1 + x = 1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.322875656 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.322875656 + 1 x = 1.322875656 + 1 Combine like terms: 1.322875656 + 1 = 2.322875656 x = 2.322875656 Simplifying x = 2.322875656Subproblem 2
x + -1 = -1.322875656 Simplifying x + -1 = -1.322875656 Reorder the terms: -1 + x = -1.322875656 Solving -1 + x = -1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.322875656 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.322875656 + 1 x = -1.322875656 + 1 Combine like terms: -1.322875656 + 1 = -0.322875656 x = -0.322875656 Simplifying x = -0.322875656Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.322875656, -0.322875656}Solution
x = {2.322875656, -0.322875656}
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