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Simplifying x2 + 5x + -88 = 0 Reorder the terms: -88 + 5x + x2 = 0 Solving -88 + 5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '88' to each side of the equation. -88 + 5x + 88 + x2 = 0 + 88 Reorder the terms: -88 + 88 + 5x + x2 = 0 + 88 Combine like terms: -88 + 88 = 0 0 + 5x + x2 = 0 + 88 5x + x2 = 0 + 88 Combine like terms: 0 + 88 = 88 5x + x2 = 88 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 = 88 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 88 + 6.25 Combine like terms: 88 + 6.25 = 94.25 6.25 + 5x + x2 = 94.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 94.25 Calculate the square root of the right side: 9.708243919 Break this problem into two subproblems by setting (x + 2.5) equal to 9.708243919 and -9.708243919.Subproblem 1
x + 2.5 = 9.708243919 Simplifying x + 2.5 = 9.708243919 Reorder the terms: 2.5 + x = 9.708243919 Solving 2.5 + x = 9.708243919 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 = 9.708243919 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 9.708243919 + -2.5 x = 9.708243919 + -2.5 Combine like terms: 9.708243919 + -2.5 = 7.208243919 x = 7.208243919 Simplifying x = 7.208243919Subproblem 2
x + 2.5 = -9.708243919 Simplifying x + 2.5 = -9.708243919 Reorder the terms: 2.5 + x = -9.708243919 Solving 2.5 + x = -9.708243919 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 = -9.708243919 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -9.708243919 + -2.5 x = -9.708243919 + -2.5 Combine like terms: -9.708243919 + -2.5 = -12.208243919 x = -12.208243919 Simplifying x = -12.208243919Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.208243919, -12.208243919}
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