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Simplifying x2 + 2x + -135 = 0 Reorder the terms: -135 + 2x + x2 = 0 Solving -135 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '135' to each side of the equation. -135 + 2x + 135 + x2 = 0 + 135 Reorder the terms: -135 + 135 + 2x + x2 = 0 + 135 Combine like terms: -135 + 135 = 0 0 + 2x + x2 = 0 + 135 2x + x2 = 0 + 135 Combine like terms: 0 + 135 = 135 2x + x2 = 135 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 135 + 1 Reorder the terms: 1 + 2x + x2 = 135 + 1 Combine like terms: 135 + 1 = 136 1 + 2x + x2 = 136 Factor a perfect square on the left side: (x + 1)(x + 1) = 136 Calculate the square root of the right side: 11.66190379 Break this problem into two subproblems by setting (x + 1) equal to 11.66190379 and -11.66190379.Subproblem 1
x + 1 = 11.66190379 Simplifying x + 1 = 11.66190379 Reorder the terms: 1 + x = 11.66190379 Solving 1 + x = 11.66190379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 11.66190379 + -1 Combine like terms: 1 + -1 = 0 0 + x = 11.66190379 + -1 x = 11.66190379 + -1 Combine like terms: 11.66190379 + -1 = 10.66190379 x = 10.66190379 Simplifying x = 10.66190379Subproblem 2
x + 1 = -11.66190379 Simplifying x + 1 = -11.66190379 Reorder the terms: 1 + x = -11.66190379 Solving 1 + x = -11.66190379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -11.66190379 + -1 Combine like terms: 1 + -1 = 0 0 + x = -11.66190379 + -1 x = -11.66190379 + -1 Combine like terms: -11.66190379 + -1 = -12.66190379 x = -12.66190379 Simplifying x = -12.66190379Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.66190379, -12.66190379}
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