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Simplifying x2 + -16x + -7860 = 0 Reorder the terms: -7860 + -16x + x2 = 0 Solving -7860 + -16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '7860' to each side of the equation. -7860 + -16x + 7860 + x2 = 0 + 7860 Reorder the terms: -7860 + 7860 + -16x + x2 = 0 + 7860 Combine like terms: -7860 + 7860 = 0 0 + -16x + x2 = 0 + 7860 -16x + x2 = 0 + 7860 Combine like terms: 0 + 7860 = 7860 -16x + x2 = 7860 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 = 7860 + 64 Reorder the terms: 64 + -16x + x2 = 7860 + 64 Combine like terms: 7860 + 64 = 7924 64 + -16x + x2 = 7924 Factor a perfect square on the left side: (x + -8)(x + -8) = 7924 Calculate the square root of the right side: 89.016852337 Break this problem into two subproblems by setting (x + -8) equal to 89.016852337 and -89.016852337.Subproblem 1
x + -8 = 89.016852337 Simplifying x + -8 = 89.016852337 Reorder the terms: -8 + x = 89.016852337 Solving -8 + x = 89.016852337 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 = 89.016852337 + 8 Combine like terms: -8 + 8 = 0 0 + x = 89.016852337 + 8 x = 89.016852337 + 8 Combine like terms: 89.016852337 + 8 = 97.016852337 x = 97.016852337 Simplifying x = 97.016852337Subproblem 2
x + -8 = -89.016852337 Simplifying x + -8 = -89.016852337 Reorder the terms: -8 + x = -89.016852337 Solving -8 + x = -89.016852337 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 = -89.016852337 + 8 Combine like terms: -8 + 8 = 0 0 + x = -89.016852337 + 8 x = -89.016852337 + 8 Combine like terms: -89.016852337 + 8 = -81.016852337 x = -81.016852337 Simplifying x = -81.016852337Solution
The solution to the problem is based on the solutions from the subproblems. x = {97.016852337, -81.016852337}
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