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Simplifying 0 = x2 + -8x + -87 Reorder the terms: 0 = -87 + -8x + x2 Solving 0 = -87 + -8x + x2 Solving for variable 'x'. Combine like terms: 0 + 87 = 87 87 + 8x + -1x2 = -87 + -8x + x2 + 87 + 8x + -1x2 Reorder the terms: 87 + 8x + -1x2 = -87 + 87 + -8x + 8x + x2 + -1x2 Combine like terms: -87 + 87 = 0 87 + 8x + -1x2 = 0 + -8x + 8x + x2 + -1x2 87 + 8x + -1x2 = -8x + 8x + x2 + -1x2 Combine like terms: -8x + 8x = 0 87 + 8x + -1x2 = 0 + x2 + -1x2 87 + 8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 87 + 8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -87 + -8x + x2 = 0 Move the constant term to the right: Add '87' to each side of the equation. -87 + -8x + 87 + x2 = 0 + 87 Reorder the terms: -87 + 87 + -8x + x2 = 0 + 87 Combine like terms: -87 + 87 = 0 0 + -8x + x2 = 0 + 87 -8x + x2 = 0 + 87 Combine like terms: 0 + 87 = 87 -8x + x2 = 87 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 = 87 + 16 Reorder the terms: 16 + -8x + x2 = 87 + 16 Combine like terms: 87 + 16 = 103 16 + -8x + x2 = 103 Factor a perfect square on the left side: (x + -4)(x + -4) = 103 Calculate the square root of the right side: 10.148891565 Break this problem into two subproblems by setting (x + -4) equal to 10.148891565 and -10.148891565.Subproblem 1
x + -4 = 10.148891565 Simplifying x + -4 = 10.148891565 Reorder the terms: -4 + x = 10.148891565 Solving -4 + x = 10.148891565 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 = 10.148891565 + 4 Combine like terms: -4 + 4 = 0 0 + x = 10.148891565 + 4 x = 10.148891565 + 4 Combine like terms: 10.148891565 + 4 = 14.148891565 x = 14.148891565 Simplifying x = 14.148891565Subproblem 2
x + -4 = -10.148891565 Simplifying x + -4 = -10.148891565 Reorder the terms: -4 + x = -10.148891565 Solving -4 + x = -10.148891565 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 = -10.148891565 + 4 Combine like terms: -4 + 4 = 0 0 + x = -10.148891565 + 4 x = -10.148891565 + 4 Combine like terms: -10.148891565 + 4 = -6.148891565 x = -6.148891565 Simplifying x = -6.148891565Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.148891565, -6.148891565}
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