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Simplifying x2 + 20x = -9 Reorder the terms: 20x + x2 = -9 Solving 20x + x2 = -9 Solving for variable 'x'. Reorder the terms: 9 + 20x + x2 = -9 + 9 Combine like terms: -9 + 9 = 0 9 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 20x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + 20x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 20x + x2 = 0 + -9 20x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 20x + x2 = -9 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 = -9 + 100 Reorder the terms: 100 + 20x + x2 = -9 + 100 Combine like terms: -9 + 100 = 91 100 + 20x + x2 = 91 Factor a perfect square on the left side: (x + 10)(x + 10) = 91 Calculate the square root of the right side: 9.539392014 Break this problem into two subproblems by setting (x + 10) equal to 9.539392014 and -9.539392014.Subproblem 1
x + 10 = 9.539392014 Simplifying x + 10 = 9.539392014 Reorder the terms: 10 + x = 9.539392014 Solving 10 + x = 9.539392014 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 = 9.539392014 + -10 Combine like terms: 10 + -10 = 0 0 + x = 9.539392014 + -10 x = 9.539392014 + -10 Combine like terms: 9.539392014 + -10 = -0.460607986 x = -0.460607986 Simplifying x = -0.460607986Subproblem 2
x + 10 = -9.539392014 Simplifying x + 10 = -9.539392014 Reorder the terms: 10 + x = -9.539392014 Solving 10 + x = -9.539392014 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 = -9.539392014 + -10 Combine like terms: 10 + -10 = 0 0 + x = -9.539392014 + -10 x = -9.539392014 + -10 Combine like terms: -9.539392014 + -10 = -19.539392014 x = -19.539392014 Simplifying x = -19.539392014Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.460607986, -19.539392014}
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