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Simplifying x2 + 32x + -1 = 75 Reorder the terms: -1 + 32x + x2 = 75 Solving -1 + 32x + x2 = 75 Solving for variable 'x'. Reorder the terms: -1 + -75 + 32x + x2 = 75 + -75 Combine like terms: -1 + -75 = -76 -76 + 32x + x2 = 75 + -75 Combine like terms: 75 + -75 = 0 -76 + 32x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '76' to each side of the equation. -76 + 32x + 76 + x2 = 0 + 76 Reorder the terms: -76 + 76 + 32x + x2 = 0 + 76 Combine like terms: -76 + 76 = 0 0 + 32x + x2 = 0 + 76 32x + x2 = 0 + 76 Combine like terms: 0 + 76 = 76 32x + x2 = 76 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 = 76 + 256 Reorder the terms: 256 + 32x + x2 = 76 + 256 Combine like terms: 76 + 256 = 332 256 + 32x + x2 = 332 Factor a perfect square on the left side: (x + 16)(x + 16) = 332 Calculate the square root of the right side: 18.220867158 Break this problem into two subproblems by setting (x + 16) equal to 18.220867158 and -18.220867158.Subproblem 1
x + 16 = 18.220867158 Simplifying x + 16 = 18.220867158 Reorder the terms: 16 + x = 18.220867158 Solving 16 + x = 18.220867158 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 = 18.220867158 + -16 Combine like terms: 16 + -16 = 0 0 + x = 18.220867158 + -16 x = 18.220867158 + -16 Combine like terms: 18.220867158 + -16 = 2.220867158 x = 2.220867158 Simplifying x = 2.220867158Subproblem 2
x + 16 = -18.220867158 Simplifying x + 16 = -18.220867158 Reorder the terms: 16 + x = -18.220867158 Solving 16 + x = -18.220867158 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 = -18.220867158 + -16 Combine like terms: 16 + -16 = 0 0 + x = -18.220867158 + -16 x = -18.220867158 + -16 Combine like terms: -18.220867158 + -16 = -34.220867158 x = -34.220867158 Simplifying x = -34.220867158Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.220867158, -34.220867158}
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