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Simplifying x2 + 81 = -20x Reorder the terms: 81 + x2 = -20x Solving 81 + x2 = -20x Solving for variable 'x'. Reorder the terms: 81 + 20x + x2 = -20x + 20x Combine like terms: -20x + 20x = 0 81 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-81' to each side of the equation. 81 + 20x + -81 + x2 = 0 + -81 Reorder the terms: 81 + -81 + 20x + x2 = 0 + -81 Combine like terms: 81 + -81 = 0 0 + 20x + x2 = 0 + -81 20x + x2 = 0 + -81 Combine like terms: 0 + -81 = -81 20x + x2 = -81 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 = -81 + 100 Reorder the terms: 100 + 20x + x2 = -81 + 100 Combine like terms: -81 + 100 = 19 100 + 20x + x2 = 19 Factor a perfect square on the left side: (x + 10)(x + 10) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (x + 10) equal to 4.358898944 and -4.358898944.Subproblem 1
x + 10 = 4.358898944 Simplifying x + 10 = 4.358898944 Reorder the terms: 10 + x = 4.358898944 Solving 10 + x = 4.358898944 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 = 4.358898944 + -10 Combine like terms: 10 + -10 = 0 0 + x = 4.358898944 + -10 x = 4.358898944 + -10 Combine like terms: 4.358898944 + -10 = -5.641101056 x = -5.641101056 Simplifying x = -5.641101056Subproblem 2
x + 10 = -4.358898944 Simplifying x + 10 = -4.358898944 Reorder the terms: 10 + x = -4.358898944 Solving 10 + x = -4.358898944 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 = -4.358898944 + -10 Combine like terms: 10 + -10 = 0 0 + x = -4.358898944 + -10 x = -4.358898944 + -10 Combine like terms: -4.358898944 + -10 = -14.358898944 x = -14.358898944 Simplifying x = -14.358898944Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.641101056, -14.358898944}
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