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Simplifying x2 + -112 = 20x Reorder the terms: -112 + x2 = 20x Solving -112 + x2 = 20x Solving for variable 'x'. Reorder the terms: -112 + -20x + x2 = 20x + -20x Combine like terms: 20x + -20x = 0 -112 + -20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '112' to each side of the equation. -112 + -20x + 112 + x2 = 0 + 112 Reorder the terms: -112 + 112 + -20x + x2 = 0 + 112 Combine like terms: -112 + 112 = 0 0 + -20x + x2 = 0 + 112 -20x + x2 = 0 + 112 Combine like terms: 0 + 112 = 112 -20x + x2 = 112 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 = 112 + 100 Reorder the terms: 100 + -20x + x2 = 112 + 100 Combine like terms: 112 + 100 = 212 100 + -20x + x2 = 212 Factor a perfect square on the left side: (x + -10)(x + -10) = 212 Calculate the square root of the right side: 14.560219779 Break this problem into two subproblems by setting (x + -10) equal to 14.560219779 and -14.560219779.Subproblem 1
x + -10 = 14.560219779 Simplifying x + -10 = 14.560219779 Reorder the terms: -10 + x = 14.560219779 Solving -10 + x = 14.560219779 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 = 14.560219779 + 10 Combine like terms: -10 + 10 = 0 0 + x = 14.560219779 + 10 x = 14.560219779 + 10 Combine like terms: 14.560219779 + 10 = 24.560219779 x = 24.560219779 Simplifying x = 24.560219779Subproblem 2
x + -10 = -14.560219779 Simplifying x + -10 = -14.560219779 Reorder the terms: -10 + x = -14.560219779 Solving -10 + x = -14.560219779 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 = -14.560219779 + 10 Combine like terms: -10 + 10 = 0 0 + x = -14.560219779 + 10 x = -14.560219779 + 10 Combine like terms: -14.560219779 + 10 = -4.560219779 x = -4.560219779 Simplifying x = -4.560219779Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.560219779, -4.560219779}
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