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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 = 319 256 + 32x + x2 = 319 Factor a perfect square on the left side: (x + 16)(x + 16) = 319 Calculate the square root of the right side: 17.860571099 Break this problem into two subproblems by setting (x + 16) equal to 17.860571099 and -17.860571099.Subproblem 1
x + 16 = 17.860571099 Simplifying x + 16 = 17.860571099 Reorder the terms: 16 + x = 17.860571099 Solving 16 + x = 17.860571099 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 = 17.860571099 + -16 Combine like terms: 16 + -16 = 0 0 + x = 17.860571099 + -16 x = 17.860571099 + -16 Combine like terms: 17.860571099 + -16 = 1.860571099 x = 1.860571099 Simplifying x = 1.860571099Subproblem 2
x + 16 = -17.860571099 Simplifying x + 16 = -17.860571099 Reorder the terms: 16 + x = -17.860571099 Solving 16 + x = -17.860571099 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 = -17.860571099 + -16 Combine like terms: 16 + -16 = 0 0 + x = -17.860571099 + -16 x = -17.860571099 + -16 Combine like terms: -17.860571099 + -16 = -33.860571099 x = -33.860571099 Simplifying x = -33.860571099Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.860571099, -33.860571099}
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