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Simplifying x2 + -20x = -11 Reorder the terms: -20x + x2 = -11 Solving -20x + x2 = -11 Solving for variable 'x'. Reorder the terms: 11 + -20x + x2 = -11 + 11 Combine like terms: -11 + 11 = 0 11 + -20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + -20x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + -20x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -20x + x2 = 0 + -11 -20x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 -20x + x2 = -11 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 = -11 + 100 Reorder the terms: 100 + -20x + x2 = -11 + 100 Combine like terms: -11 + 100 = 89 100 + -20x + x2 = 89 Factor a perfect square on the left side: (x + -10)(x + -10) = 89 Calculate the square root of the right side: 9.433981132 Break this problem into two subproblems by setting (x + -10) equal to 9.433981132 and -9.433981132.Subproblem 1
x + -10 = 9.433981132 Simplifying x + -10 = 9.433981132 Reorder the terms: -10 + x = 9.433981132 Solving -10 + x = 9.433981132 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 = 9.433981132 + 10 Combine like terms: -10 + 10 = 0 0 + x = 9.433981132 + 10 x = 9.433981132 + 10 Combine like terms: 9.433981132 + 10 = 19.433981132 x = 19.433981132 Simplifying x = 19.433981132Subproblem 2
x + -10 = -9.433981132 Simplifying x + -10 = -9.433981132 Reorder the terms: -10 + x = -9.433981132 Solving -10 + x = -9.433981132 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 = -9.433981132 + 10 Combine like terms: -10 + 10 = 0 0 + x = -9.433981132 + 10 x = -9.433981132 + 10 Combine like terms: -9.433981132 + 10 = 0.566018868 x = 0.566018868 Simplifying x = 0.566018868Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.433981132, 0.566018868}
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