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Simplifying 0 = 4x2 + 2x + -64 Reorder the terms: 0 = -64 + 2x + 4x2 Solving 0 = -64 + 2x + 4x2 Solving for variable 'x'. Combine like terms: 0 + 64 = 64 64 + -2x + -4x2 = -64 + 2x + 4x2 + 64 + -2x + -4x2 Reorder the terms: 64 + -2x + -4x2 = -64 + 64 + 2x + -2x + 4x2 + -4x2 Combine like terms: -64 + 64 = 0 64 + -2x + -4x2 = 0 + 2x + -2x + 4x2 + -4x2 64 + -2x + -4x2 = 2x + -2x + 4x2 + -4x2 Combine like terms: 2x + -2x = 0 64 + -2x + -4x2 = 0 + 4x2 + -4x2 64 + -2x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 64 + -2x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(32 + -1x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(32 + -1x + -2x2)' equal to zero and attempt to solve: Simplifying 32 + -1x + -2x2 = 0 Solving 32 + -1x + -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 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 16 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 16 + 0.0625 Combine like terms: 16 + 0.0625 = 16.0625 0.0625 + 0.5x + x2 = 16.0625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 16.0625 Calculate the square root of the right side: 4.007804885 Break this problem into two subproblems by setting (x + 0.25) equal to 4.007804885 and -4.007804885.Subproblem 1
x + 0.25 = 4.007804885 Simplifying x + 0.25 = 4.007804885 Reorder the terms: 0.25 + x = 4.007804885 Solving 0.25 + x = 4.007804885 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 4.007804885 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 4.007804885 + -0.25 x = 4.007804885 + -0.25 Combine like terms: 4.007804885 + -0.25 = 3.757804885 x = 3.757804885 Simplifying x = 3.757804885Subproblem 2
x + 0.25 = -4.007804885 Simplifying x + 0.25 = -4.007804885 Reorder the terms: 0.25 + x = -4.007804885 Solving 0.25 + x = -4.007804885 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -4.007804885 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -4.007804885 + -0.25 x = -4.007804885 + -0.25 Combine like terms: -4.007804885 + -0.25 = -4.257804885 x = -4.257804885 Simplifying x = -4.257804885Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.757804885, -4.257804885}Solution
x = {3.757804885, -4.257804885}
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