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Simplifying 8x2 + 32x + -512 = 0 Reorder the terms: -512 + 32x + 8x2 = 0 Solving -512 + 32x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(-64 + 4x + x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-64 + 4x + x2)' equal to zero and attempt to solve: Simplifying -64 + 4x + x2 = 0 Solving -64 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + 4x + 64 + x2 = 0 + 64 Reorder the terms: -64 + 64 + 4x + x2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 4x + x2 = 0 + 64 4x + x2 = 0 + 64 Combine like terms: 0 + 64 = 64 4x + x2 = 64 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 = 64 + 4 Reorder the terms: 4 + 4x + x2 = 64 + 4 Combine like terms: 64 + 4 = 68 4 + 4x + x2 = 68 Factor a perfect square on the left side: (x + 2)(x + 2) = 68 Calculate the square root of the right side: 8.246211251 Break this problem into two subproblems by setting (x + 2) equal to 8.246211251 and -8.246211251.Subproblem 1
x + 2 = 8.246211251 Simplifying x + 2 = 8.246211251 Reorder the terms: 2 + x = 8.246211251 Solving 2 + x = 8.246211251 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 = 8.246211251 + -2 Combine like terms: 2 + -2 = 0 0 + x = 8.246211251 + -2 x = 8.246211251 + -2 Combine like terms: 8.246211251 + -2 = 6.246211251 x = 6.246211251 Simplifying x = 6.246211251Subproblem 2
x + 2 = -8.246211251 Simplifying x + 2 = -8.246211251 Reorder the terms: 2 + x = -8.246211251 Solving 2 + x = -8.246211251 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 = -8.246211251 + -2 Combine like terms: 2 + -2 = 0 0 + x = -8.246211251 + -2 x = -8.246211251 + -2 Combine like terms: -8.246211251 + -2 = -10.246211251 x = -10.246211251 Simplifying x = -10.246211251Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.246211251, -10.246211251}Solution
x = {6.246211251, -10.246211251}
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