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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 = 5.25 4 + -4x + x2 = 5.25 Factor a perfect square on the left side: (x + -2)(x + -2) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (x + -2) equal to 2.291287847 and -2.291287847.Subproblem 1
x + -2 = 2.291287847 Simplifying x + -2 = 2.291287847 Reorder the terms: -2 + x = 2.291287847 Solving -2 + x = 2.291287847 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 = 2.291287847 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.291287847 + 2 x = 2.291287847 + 2 Combine like terms: 2.291287847 + 2 = 4.291287847 x = 4.291287847 Simplifying x = 4.291287847Subproblem 2
x + -2 = -2.291287847 Simplifying x + -2 = -2.291287847 Reorder the terms: -2 + x = -2.291287847 Solving -2 + x = -2.291287847 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 = -2.291287847 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.291287847 + 2 x = -2.291287847 + 2 Combine like terms: -2.291287847 + 2 = -0.291287847 x = -0.291287847 Simplifying x = -0.291287847Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.291287847, -0.291287847}Solution
x = {4.291287847, -0.291287847}
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