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Simplifying x2 + 87 = -20x Reorder the terms: 87 + x2 = -20x Solving 87 + x2 = -20x Solving for variable 'x'. Reorder the terms: 87 + 20x + x2 = -20x + 20x Combine like terms: -20x + 20x = 0 87 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-87' to each side of the equation. 87 + 20x + -87 + x2 = 0 + -87 Reorder the terms: 87 + -87 + 20x + x2 = 0 + -87 Combine like terms: 87 + -87 = 0 0 + 20x + x2 = 0 + -87 20x + x2 = 0 + -87 Combine like terms: 0 + -87 = -87 20x + x2 = -87 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 = -87 + 100 Reorder the terms: 100 + 20x + x2 = -87 + 100 Combine like terms: -87 + 100 = 13 100 + 20x + x2 = 13 Factor a perfect square on the left side: (x + 10)(x + 10) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (x + 10) equal to 3.605551275 and -3.605551275.Subproblem 1
x + 10 = 3.605551275 Simplifying x + 10 = 3.605551275 Reorder the terms: 10 + x = 3.605551275 Solving 10 + x = 3.605551275 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 = 3.605551275 + -10 Combine like terms: 10 + -10 = 0 0 + x = 3.605551275 + -10 x = 3.605551275 + -10 Combine like terms: 3.605551275 + -10 = -6.394448725 x = -6.394448725 Simplifying x = -6.394448725Subproblem 2
x + 10 = -3.605551275 Simplifying x + 10 = -3.605551275 Reorder the terms: 10 + x = -3.605551275 Solving 10 + x = -3.605551275 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 = -3.605551275 + -10 Combine like terms: 10 + -10 = 0 0 + x = -3.605551275 + -10 x = -3.605551275 + -10 Combine like terms: -3.605551275 + -10 = -13.605551275 x = -13.605551275 Simplifying x = -13.605551275Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.394448725, -13.605551275}
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