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Simplifying x2 + 20x = -8 Reorder the terms: 20x + x2 = -8 Solving 20x + x2 = -8 Solving for variable 'x'. Reorder the terms: 8 + 20x + x2 = -8 + 8 Combine like terms: -8 + 8 = 0 8 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + 20x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + 20x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 20x + x2 = 0 + -8 20x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 20x + x2 = -8 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 = -8 + 100 Reorder the terms: 100 + 20x + x2 = -8 + 100 Combine like terms: -8 + 100 = 92 100 + 20x + x2 = 92 Factor a perfect square on the left side: (x + 10)(x + 10) = 92 Calculate the square root of the right side: 9.591663047 Break this problem into two subproblems by setting (x + 10) equal to 9.591663047 and -9.591663047.Subproblem 1
x + 10 = 9.591663047 Simplifying x + 10 = 9.591663047 Reorder the terms: 10 + x = 9.591663047 Solving 10 + x = 9.591663047 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 = 9.591663047 + -10 Combine like terms: 10 + -10 = 0 0 + x = 9.591663047 + -10 x = 9.591663047 + -10 Combine like terms: 9.591663047 + -10 = -0.408336953 x = -0.408336953 Simplifying x = -0.408336953Subproblem 2
x + 10 = -9.591663047 Simplifying x + 10 = -9.591663047 Reorder the terms: 10 + x = -9.591663047 Solving 10 + x = -9.591663047 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 = -9.591663047 + -10 Combine like terms: 10 + -10 = 0 0 + x = -9.591663047 + -10 x = -9.591663047 + -10 Combine like terms: -9.591663047 + -10 = -19.591663047 x = -19.591663047 Simplifying x = -19.591663047Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.408336953, -19.591663047}
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