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Simplifying x2 + 20x = -18 Reorder the terms: 20x + x2 = -18 Solving 20x + x2 = -18 Solving for variable 'x'. Reorder the terms: 18 + 20x + x2 = -18 + 18 Combine like terms: -18 + 18 = 0 18 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + 20x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + 20x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + 20x + x2 = 0 + -18 20x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 20x + x2 = -18 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 = -18 + 100 Reorder the terms: 100 + 20x + x2 = -18 + 100 Combine like terms: -18 + 100 = 82 100 + 20x + x2 = 82 Factor a perfect square on the left side: (x + 10)(x + 10) = 82 Calculate the square root of the right side: 9.055385138 Break this problem into two subproblems by setting (x + 10) equal to 9.055385138 and -9.055385138.Subproblem 1
x + 10 = 9.055385138 Simplifying x + 10 = 9.055385138 Reorder the terms: 10 + x = 9.055385138 Solving 10 + x = 9.055385138 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 = 9.055385138 + -10 Combine like terms: 10 + -10 = 0 0 + x = 9.055385138 + -10 x = 9.055385138 + -10 Combine like terms: 9.055385138 + -10 = -0.944614862 x = -0.944614862 Simplifying x = -0.944614862Subproblem 2
x + 10 = -9.055385138 Simplifying x + 10 = -9.055385138 Reorder the terms: 10 + x = -9.055385138 Solving 10 + x = -9.055385138 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 = -9.055385138 + -10 Combine like terms: 10 + -10 = 0 0 + x = -9.055385138 + -10 x = -9.055385138 + -10 Combine like terms: -9.055385138 + -10 = -19.055385138 x = -19.055385138 Simplifying x = -19.055385138Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.944614862, -19.055385138}
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