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Simplifying 4x2 + 2x + -64 = 0 Reorder the terms: -64 + 2x + 4x2 = 0 Solving -64 + 2x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-32 + x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-32 + x + 2x2)' equal to zero and attempt to solve: Simplifying -32 + x + 2x2 = 0 Solving -32 + x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -16 + 0.5x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + 0.5x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 0.5x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 0.5x + x2 = 0 + 16 0.5x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 0.5x + 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. 0.5x + 0.25 + x2 = 16 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = 16 + 0.25 Combine like terms: 16 + 0.25 = 16.25 0.25 + 0.5x + 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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