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Simplifying 0 = 4x2 + 4x + -64 Reorder the terms: 0 = -64 + 4x + 4x2 Solving 0 = -64 + 4x + 4x2 Solving for variable 'x'. Combine like terms: 0 + 64 = 64 64 + -4x + -4x2 = -64 + 4x + 4x2 + 64 + -4x + -4x2 Reorder the terms: 64 + -4x + -4x2 = -64 + 64 + 4x + -4x + 4x2 + -4x2 Combine like terms: -64 + 64 = 0 64 + -4x + -4x2 = 0 + 4x + -4x + 4x2 + -4x2 64 + -4x + -4x2 = 4x + -4x + 4x2 + -4x2 Combine like terms: 4x + -4x = 0 64 + -4x + -4x2 = 0 + 4x2 + -4x2 64 + -4x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 64 + -4x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(16 + -1x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(16 + -1x + -1x2)' equal to zero and attempt to solve: Simplifying 16 + -1x + -1x2 = 0 Solving 16 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -16 + x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + x + x2 = 0 + 16 x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 x + x2 = 16 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 16 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 16 + 0.25 Combine like terms: 16 + 0.25 = 16.25 1.25 + x2 = 16.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (x + 0.5) equal to 4.031128874 and -4.031128874.Subproblem 1
x + 0.5 = 4.031128874 Simplifying x + 0.5 = 4.031128874 Reorder the terms: 0.5 + x = 4.031128874 Solving 0.5 + x = 4.031128874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 4.031128874 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.031128874 + -0.5 x = 4.031128874 + -0.5 Combine like terms: 4.031128874 + -0.5 = 3.531128874 x = 3.531128874 Simplifying x = 3.531128874Subproblem 2
x + 0.5 = -4.031128874 Simplifying x + 0.5 = -4.031128874 Reorder the terms: 0.5 + x = -4.031128874 Solving 0.5 + x = -4.031128874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -4.031128874 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.031128874 + -0.5 x = -4.031128874 + -0.5 Combine like terms: -4.031128874 + -0.5 = -4.531128874 x = -4.531128874 Simplifying x = -4.531128874Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.531128874, -4.531128874}Solution
x = {3.531128874, -4.531128874}
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