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Simplifying x2 + -8x + -143 = 0 Reorder the terms: -143 + -8x + x2 = 0 Solving -143 + -8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '143' to each side of the equation. -143 + -8x + 143 + x2 = 0 + 143 Reorder the terms: -143 + 143 + -8x + x2 = 0 + 143 Combine like terms: -143 + 143 = 0 0 + -8x + x2 = 0 + 143 -8x + x2 = 0 + 143 Combine like terms: 0 + 143 = 143 -8x + x2 = 143 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 143 + 16 Reorder the terms: 16 + -8x + x2 = 143 + 16 Combine like terms: 143 + 16 = 159 16 + -8x + x2 = 159 Factor a perfect square on the left side: (x + -4)(x + -4) = 159 Calculate the square root of the right side: 12.609520213 Break this problem into two subproblems by setting (x + -4) equal to 12.609520213 and -12.609520213.Subproblem 1
x + -4 = 12.609520213 Simplifying x + -4 = 12.609520213 Reorder the terms: -4 + x = 12.609520213 Solving -4 + x = 12.609520213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 12.609520213 + 4 Combine like terms: -4 + 4 = 0 0 + x = 12.609520213 + 4 x = 12.609520213 + 4 Combine like terms: 12.609520213 + 4 = 16.609520213 x = 16.609520213 Simplifying x = 16.609520213Subproblem 2
x + -4 = -12.609520213 Simplifying x + -4 = -12.609520213 Reorder the terms: -4 + x = -12.609520213 Solving -4 + x = -12.609520213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -12.609520213 + 4 Combine like terms: -4 + 4 = 0 0 + x = -12.609520213 + 4 x = -12.609520213 + 4 Combine like terms: -12.609520213 + 4 = -8.609520213 x = -8.609520213 Simplifying x = -8.609520213Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.609520213, -8.609520213}
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