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Simplifying x2 + -32x + 256 = 37 Reorder the terms: 256 + -32x + x2 = 37 Solving 256 + -32x + x2 = 37 Solving for variable 'x'. Reorder the terms: 256 + -37 + -32x + x2 = 37 + -37 Combine like terms: 256 + -37 = 219 219 + -32x + x2 = 37 + -37 Combine like terms: 37 + -37 = 0 219 + -32x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-219' to each side of the equation. 219 + -32x + -219 + x2 = 0 + -219 Reorder the terms: 219 + -219 + -32x + x2 = 0 + -219 Combine like terms: 219 + -219 = 0 0 + -32x + x2 = 0 + -219 -32x + x2 = 0 + -219 Combine like terms: 0 + -219 = -219 -32x + x2 = -219 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 = -219 + 256 Reorder the terms: 256 + -32x + x2 = -219 + 256 Combine like terms: -219 + 256 = 37 256 + -32x + x2 = 37 Factor a perfect square on the left side: (x + -16)(x + -16) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (x + -16) equal to 6.08276253 and -6.08276253.Subproblem 1
x + -16 = 6.08276253 Simplifying x + -16 = 6.08276253 Reorder the terms: -16 + x = 6.08276253 Solving -16 + x = 6.08276253 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 = 6.08276253 + 16 Combine like terms: -16 + 16 = 0 0 + x = 6.08276253 + 16 x = 6.08276253 + 16 Combine like terms: 6.08276253 + 16 = 22.08276253 x = 22.08276253 Simplifying x = 22.08276253Subproblem 2
x + -16 = -6.08276253 Simplifying x + -16 = -6.08276253 Reorder the terms: -16 + x = -6.08276253 Solving -16 + x = -6.08276253 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 = -6.08276253 + 16 Combine like terms: -16 + 16 = 0 0 + x = -6.08276253 + 16 x = -6.08276253 + 16 Combine like terms: -6.08276253 + 16 = 9.91723747 x = 9.91723747 Simplifying x = 9.91723747Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.08276253, 9.91723747}
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