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Simplifying 0 = x2 + 5x + -86 Reorder the terms: 0 = -86 + 5x + x2 Solving 0 = -86 + 5x + x2 Solving for variable 'x'. Combine like terms: 0 + 86 = 86 86 + -5x + -1x2 = -86 + 5x + x2 + 86 + -5x + -1x2 Reorder the terms: 86 + -5x + -1x2 = -86 + 86 + 5x + -5x + x2 + -1x2 Combine like terms: -86 + 86 = 0 86 + -5x + -1x2 = 0 + 5x + -5x + x2 + -1x2 86 + -5x + -1x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 86 + -5x + -1x2 = 0 + x2 + -1x2 86 + -5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 86 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -86 + 5x + x2 = 0 Move the constant term to the right: Add '86' to each side of the equation. -86 + 5x + 86 + x2 = 0 + 86 Reorder the terms: -86 + 86 + 5x + x2 = 0 + 86 Combine like terms: -86 + 86 = 0 0 + 5x + x2 = 0 + 86 5x + x2 = 0 + 86 Combine like terms: 0 + 86 = 86 5x + x2 = 86 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 86 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 86 + 6.25 Combine like terms: 86 + 6.25 = 92.25 6.25 + 5x + x2 = 92.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 92.25 Calculate the square root of the right side: 9.604686356 Break this problem into two subproblems by setting (x + 2.5) equal to 9.604686356 and -9.604686356.Subproblem 1
x + 2.5 = 9.604686356 Simplifying x + 2.5 = 9.604686356 Reorder the terms: 2.5 + x = 9.604686356 Solving 2.5 + x = 9.604686356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 9.604686356 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 9.604686356 + -2.5 x = 9.604686356 + -2.5 Combine like terms: 9.604686356 + -2.5 = 7.104686356 x = 7.104686356 Simplifying x = 7.104686356Subproblem 2
x + 2.5 = -9.604686356 Simplifying x + 2.5 = -9.604686356 Reorder the terms: 2.5 + x = -9.604686356 Solving 2.5 + x = -9.604686356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -9.604686356 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -9.604686356 + -2.5 x = -9.604686356 + -2.5 Combine like terms: -9.604686356 + -2.5 = -12.104686356 x = -12.104686356 Simplifying x = -12.104686356Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.104686356, -12.104686356}
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