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Simplifying x2 + 32x + -69 = 0 Reorder the terms: -69 + 32x + x2 = 0 Solving -69 + 32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '69' to each side of the equation. -69 + 32x + 69 + x2 = 0 + 69 Reorder the terms: -69 + 69 + 32x + x2 = 0 + 69 Combine like terms: -69 + 69 = 0 0 + 32x + x2 = 0 + 69 32x + x2 = 0 + 69 Combine like terms: 0 + 69 = 69 32x + x2 = 69 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 = 69 + 256 Reorder the terms: 256 + 32x + x2 = 69 + 256 Combine like terms: 69 + 256 = 325 256 + 32x + x2 = 325 Factor a perfect square on the left side: (x + 16)(x + 16) = 325 Calculate the square root of the right side: 18.027756377 Break this problem into two subproblems by setting (x + 16) equal to 18.027756377 and -18.027756377.Subproblem 1
x + 16 = 18.027756377 Simplifying x + 16 = 18.027756377 Reorder the terms: 16 + x = 18.027756377 Solving 16 + x = 18.027756377 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 = 18.027756377 + -16 Combine like terms: 16 + -16 = 0 0 + x = 18.027756377 + -16 x = 18.027756377 + -16 Combine like terms: 18.027756377 + -16 = 2.027756377 x = 2.027756377 Simplifying x = 2.027756377Subproblem 2
x + 16 = -18.027756377 Simplifying x + 16 = -18.027756377 Reorder the terms: 16 + x = -18.027756377 Solving 16 + x = -18.027756377 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 = -18.027756377 + -16 Combine like terms: 16 + -16 = 0 0 + x = -18.027756377 + -16 x = -18.027756377 + -16 Combine like terms: -18.027756377 + -16 = -34.027756377 x = -34.027756377 Simplifying x = -34.027756377Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.027756377, -34.027756377}
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