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Simplifying x2 + -32x + 63 = 0 Reorder the terms: 63 + -32x + x2 = 0 Solving 63 + -32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-63' to each side of the equation. 63 + -32x + -63 + x2 = 0 + -63 Reorder the terms: 63 + -63 + -32x + x2 = 0 + -63 Combine like terms: 63 + -63 = 0 0 + -32x + x2 = 0 + -63 -32x + x2 = 0 + -63 Combine like terms: 0 + -63 = -63 -32x + x2 = -63 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 = -63 + 256 Reorder the terms: 256 + -32x + x2 = -63 + 256 Combine like terms: -63 + 256 = 193 256 + -32x + x2 = 193 Factor a perfect square on the left side: (x + -16)(x + -16) = 193 Calculate the square root of the right side: 13.892443989 Break this problem into two subproblems by setting (x + -16) equal to 13.892443989 and -13.892443989.Subproblem 1
x + -16 = 13.892443989 Simplifying x + -16 = 13.892443989 Reorder the terms: -16 + x = 13.892443989 Solving -16 + x = 13.892443989 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 = 13.892443989 + 16 Combine like terms: -16 + 16 = 0 0 + x = 13.892443989 + 16 x = 13.892443989 + 16 Combine like terms: 13.892443989 + 16 = 29.892443989 x = 29.892443989 Simplifying x = 29.892443989Subproblem 2
x + -16 = -13.892443989 Simplifying x + -16 = -13.892443989 Reorder the terms: -16 + x = -13.892443989 Solving -16 + x = -13.892443989 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 = -13.892443989 + 16 Combine like terms: -16 + 16 = 0 0 + x = -13.892443989 + 16 x = -13.892443989 + 16 Combine like terms: -13.892443989 + 16 = 2.107556011 x = 2.107556011 Simplifying x = 2.107556011Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.892443989, 2.107556011}
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