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Simplifying x2 + -32x + -360 = 0 Reorder the terms: -360 + -32x + x2 = 0 Solving -360 + -32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '360' to each side of the equation. -360 + -32x + 360 + x2 = 0 + 360 Reorder the terms: -360 + 360 + -32x + x2 = 0 + 360 Combine like terms: -360 + 360 = 0 0 + -32x + x2 = 0 + 360 -32x + x2 = 0 + 360 Combine like terms: 0 + 360 = 360 -32x + x2 = 360 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 = 360 + 256 Reorder the terms: 256 + -32x + x2 = 360 + 256 Combine like terms: 360 + 256 = 616 256 + -32x + x2 = 616 Factor a perfect square on the left side: (x + -16)(x + -16) = 616 Calculate the square root of the right side: 24.819347292 Break this problem into two subproblems by setting (x + -16) equal to 24.819347292 and -24.819347292.Subproblem 1
x + -16 = 24.819347292 Simplifying x + -16 = 24.819347292 Reorder the terms: -16 + x = 24.819347292 Solving -16 + x = 24.819347292 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 = 24.819347292 + 16 Combine like terms: -16 + 16 = 0 0 + x = 24.819347292 + 16 x = 24.819347292 + 16 Combine like terms: 24.819347292 + 16 = 40.819347292 x = 40.819347292 Simplifying x = 40.819347292Subproblem 2
x + -16 = -24.819347292 Simplifying x + -16 = -24.819347292 Reorder the terms: -16 + x = -24.819347292 Solving -16 + x = -24.819347292 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 = -24.819347292 + 16 Combine like terms: -16 + 16 = 0 0 + x = -24.819347292 + 16 x = -24.819347292 + 16 Combine like terms: -24.819347292 + 16 = -8.819347292 x = -8.819347292 Simplifying x = -8.819347292Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.819347292, -8.819347292}
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