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Simplifying 2x2 + 64x = 2 Reorder the terms: 64x + 2x2 = 2 Solving 64x + 2x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + 64x + 2x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 64x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 32x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 32x + x2)' equal to zero and attempt to solve: Simplifying -1 + 32x + x2 = 0 Solving -1 + 32x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 32x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 32x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 32x + x2 = 0 + 1 32x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 32x + x2 = 1 The x term is 32x. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32x + 256 + x2 = 1 + 256 Reorder the terms: 256 + 32x + x2 = 1 + 256 Combine like terms: 1 + 256 = 257 256 + 32x + x2 = 257 Factor a perfect square on the left side: (x + 16)(x + 16) = 257 Calculate the square root of the right side: 16.031219542 Break this problem into two subproblems by setting (x + 16) equal to 16.031219542 and -16.031219542.Subproblem 1
x + 16 = 16.031219542 Simplifying x + 16 = 16.031219542 Reorder the terms: 16 + x = 16.031219542 Solving 16 + x = 16.031219542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = 16.031219542 + -16 Combine like terms: 16 + -16 = 0 0 + x = 16.031219542 + -16 x = 16.031219542 + -16 Combine like terms: 16.031219542 + -16 = 0.031219542 x = 0.031219542 Simplifying x = 0.031219542Subproblem 2
x + 16 = -16.031219542 Simplifying x + 16 = -16.031219542 Reorder the terms: 16 + x = -16.031219542 Solving 16 + x = -16.031219542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = -16.031219542 + -16 Combine like terms: 16 + -16 = 0 0 + x = -16.031219542 + -16 x = -16.031219542 + -16 Combine like terms: -16.031219542 + -16 = -32.031219542 x = -32.031219542 Simplifying x = -32.031219542Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.031219542, -32.031219542}Solution
x = {0.031219542, -32.031219542}
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