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Simplifying x2 + 20x + -36 = 0 Reorder the terms: -36 + 20x + x2 = 0 Solving -36 + 20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 20x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + 20x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 20x + x2 = 0 + 36 20x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 20x + x2 = 36 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 36 + 100 Reorder the terms: 100 + 20x + x2 = 36 + 100 Combine like terms: 36 + 100 = 136 100 + 20x + x2 = 136 Factor a perfect square on the left side: (x + 10)(x + 10) = 136 Calculate the square root of the right side: 11.66190379 Break this problem into two subproblems by setting (x + 10) equal to 11.66190379 and -11.66190379.Subproblem 1
x + 10 = 11.66190379 Simplifying x + 10 = 11.66190379 Reorder the terms: 10 + x = 11.66190379 Solving 10 + x = 11.66190379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 11.66190379 + -10 Combine like terms: 10 + -10 = 0 0 + x = 11.66190379 + -10 x = 11.66190379 + -10 Combine like terms: 11.66190379 + -10 = 1.66190379 x = 1.66190379 Simplifying x = 1.66190379Subproblem 2
x + 10 = -11.66190379 Simplifying x + 10 = -11.66190379 Reorder the terms: 10 + x = -11.66190379 Solving 10 + x = -11.66190379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -11.66190379 + -10 Combine like terms: 10 + -10 = 0 0 + x = -11.66190379 + -10 x = -11.66190379 + -10 Combine like terms: -11.66190379 + -10 = -21.66190379 x = -21.66190379 Simplifying x = -21.66190379Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.66190379, -21.66190379}
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