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Simplifying x2 + -16x + -312 = 0 Reorder the terms: -312 + -16x + x2 = 0 Solving -312 + -16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '312' to each side of the equation. -312 + -16x + 312 + x2 = 0 + 312 Reorder the terms: -312 + 312 + -16x + x2 = 0 + 312 Combine like terms: -312 + 312 = 0 0 + -16x + x2 = 0 + 312 -16x + x2 = 0 + 312 Combine like terms: 0 + 312 = 312 -16x + x2 = 312 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = 312 + 64 Reorder the terms: 64 + -16x + x2 = 312 + 64 Combine like terms: 312 + 64 = 376 64 + -16x + x2 = 376 Factor a perfect square on the left side: (x + -8)(x + -8) = 376 Calculate the square root of the right side: 19.39071943 Break this problem into two subproblems by setting (x + -8) equal to 19.39071943 and -19.39071943.Subproblem 1
x + -8 = 19.39071943 Simplifying x + -8 = 19.39071943 Reorder the terms: -8 + x = 19.39071943 Solving -8 + x = 19.39071943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 19.39071943 + 8 Combine like terms: -8 + 8 = 0 0 + x = 19.39071943 + 8 x = 19.39071943 + 8 Combine like terms: 19.39071943 + 8 = 27.39071943 x = 27.39071943 Simplifying x = 27.39071943Subproblem 2
x + -8 = -19.39071943 Simplifying x + -8 = -19.39071943 Reorder the terms: -8 + x = -19.39071943 Solving -8 + x = -19.39071943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -19.39071943 + 8 Combine like terms: -8 + 8 = 0 0 + x = -19.39071943 + 8 x = -19.39071943 + 8 Combine like terms: -19.39071943 + 8 = -11.39071943 x = -11.39071943 Simplifying x = -11.39071943Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.39071943, -11.39071943}
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