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Simplifying x2 + -32x + 40 = 0 Reorder the terms: 40 + -32x + x2 = 0 Solving 40 + -32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-40' to each side of the equation. 40 + -32x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + -32x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -32x + x2 = 0 + -40 -32x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 -32x + x2 = -40 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 = -40 + 256 Reorder the terms: 256 + -32x + x2 = -40 + 256 Combine like terms: -40 + 256 = 216 256 + -32x + x2 = 216 Factor a perfect square on the left side: (x + -16)(x + -16) = 216 Calculate the square root of the right side: 14.696938457 Break this problem into two subproblems by setting (x + -16) equal to 14.696938457 and -14.696938457.Subproblem 1
x + -16 = 14.696938457 Simplifying x + -16 = 14.696938457 Reorder the terms: -16 + x = 14.696938457 Solving -16 + x = 14.696938457 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 = 14.696938457 + 16 Combine like terms: -16 + 16 = 0 0 + x = 14.696938457 + 16 x = 14.696938457 + 16 Combine like terms: 14.696938457 + 16 = 30.696938457 x = 30.696938457 Simplifying x = 30.696938457Subproblem 2
x + -16 = -14.696938457 Simplifying x + -16 = -14.696938457 Reorder the terms: -16 + x = -14.696938457 Solving -16 + x = -14.696938457 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 = -14.696938457 + 16 Combine like terms: -16 + 16 = 0 0 + x = -14.696938457 + 16 x = -14.696938457 + 16 Combine like terms: -14.696938457 + 16 = 1.303061543 x = 1.303061543 Simplifying x = 1.303061543Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.696938457, 1.303061543}
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