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Simplifying -16x2 + 64x + -20 = 0 Reorder the terms: -20 + 64x + -16x2 = 0 Solving -20 + 64x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + 16x + -4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + 16x + -4x2)' equal to zero and attempt to solve: Simplifying -5 + 16x + -4x2 = 0 Solving -5 + 16x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 1.25 + -4x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -4x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -4x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -4x + x2 = 0 + -1.25 -4x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -4x + x2 = -1.25 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -1.25 + 4 Reorder the terms: 4 + -4x + x2 = -1.25 + 4 Combine like terms: -1.25 + 4 = 2.75 4 + -4x + x2 = 2.75 Factor a perfect square on the left side: (x + -2)(x + -2) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (x + -2) equal to 1.658312395 and -1.658312395.Subproblem 1
x + -2 = 1.658312395 Simplifying x + -2 = 1.658312395 Reorder the terms: -2 + x = 1.658312395 Solving -2 + x = 1.658312395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.658312395 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.658312395 + 2 x = 1.658312395 + 2 Combine like terms: 1.658312395 + 2 = 3.658312395 x = 3.658312395 Simplifying x = 3.658312395Subproblem 2
x + -2 = -1.658312395 Simplifying x + -2 = -1.658312395 Reorder the terms: -2 + x = -1.658312395 Solving -2 + x = -1.658312395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.658312395 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.658312395 + 2 x = -1.658312395 + 2 Combine like terms: -1.658312395 + 2 = 0.341687605 x = 0.341687605 Simplifying x = 0.341687605Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.658312395, 0.341687605}Solution
x = {3.658312395, 0.341687605}
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