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Simplifying 32x + x2 = 256 Solving 32x + x2 = 256 Solving for variable 'x'. Reorder the terms: -256 + 32x + x2 = 256 + -256 Combine like terms: 256 + -256 = 0 -256 + 32x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '256' to each side of the equation. -256 + 32x + 256 + x2 = 0 + 256 Reorder the terms: -256 + 256 + 32x + x2 = 0 + 256 Combine like terms: -256 + 256 = 0 0 + 32x + x2 = 0 + 256 32x + x2 = 0 + 256 Combine like terms: 0 + 256 = 256 32x + x2 = 256 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 = 256 + 256 Reorder the terms: 256 + 32x + x2 = 256 + 256 Combine like terms: 256 + 256 = 512 256 + 32x + x2 = 512 Factor a perfect square on the left side: (x + 16)(x + 16) = 512 Calculate the square root of the right side: 22.627416998 Break this problem into two subproblems by setting (x + 16) equal to 22.627416998 and -22.627416998.Subproblem 1
x + 16 = 22.627416998 Simplifying x + 16 = 22.627416998 Reorder the terms: 16 + x = 22.627416998 Solving 16 + x = 22.627416998 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 = 22.627416998 + -16 Combine like terms: 16 + -16 = 0 0 + x = 22.627416998 + -16 x = 22.627416998 + -16 Combine like terms: 22.627416998 + -16 = 6.627416998 x = 6.627416998 Simplifying x = 6.627416998Subproblem 2
x + 16 = -22.627416998 Simplifying x + 16 = -22.627416998 Reorder the terms: 16 + x = -22.627416998 Solving 16 + x = -22.627416998 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 = -22.627416998 + -16 Combine like terms: 16 + -16 = 0 0 + x = -22.627416998 + -16 x = -22.627416998 + -16 Combine like terms: -22.627416998 + -16 = -38.627416998 x = -38.627416998 Simplifying x = -38.627416998Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.627416998, -38.627416998}
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