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Simplifying x2 + 20x = 99 Reorder the terms: 20x + x2 = 99 Solving 20x + x2 = 99 Solving for variable 'x'. Reorder the terms: -99 + 20x + x2 = 99 + -99 Combine like terms: 99 + -99 = 0 -99 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '99' to each side of the equation. -99 + 20x + 99 + x2 = 0 + 99 Reorder the terms: -99 + 99 + 20x + x2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + 20x + x2 = 0 + 99 20x + x2 = 0 + 99 Combine like terms: 0 + 99 = 99 20x + x2 = 99 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 = 99 + 100 Reorder the terms: 100 + 20x + x2 = 99 + 100 Combine like terms: 99 + 100 = 199 100 + 20x + x2 = 199 Factor a perfect square on the left side: (x + 10)(x + 10) = 199 Calculate the square root of the right side: 14.10673598 Break this problem into two subproblems by setting (x + 10) equal to 14.10673598 and -14.10673598.Subproblem 1
x + 10 = 14.10673598 Simplifying x + 10 = 14.10673598 Reorder the terms: 10 + x = 14.10673598 Solving 10 + x = 14.10673598 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 = 14.10673598 + -10 Combine like terms: 10 + -10 = 0 0 + x = 14.10673598 + -10 x = 14.10673598 + -10 Combine like terms: 14.10673598 + -10 = 4.10673598 x = 4.10673598 Simplifying x = 4.10673598Subproblem 2
x + 10 = -14.10673598 Simplifying x + 10 = -14.10673598 Reorder the terms: 10 + x = -14.10673598 Solving 10 + x = -14.10673598 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 = -14.10673598 + -10 Combine like terms: 10 + -10 = 0 0 + x = -14.10673598 + -10 x = -14.10673598 + -10 Combine like terms: -14.10673598 + -10 = -24.10673598 x = -24.10673598 Simplifying x = -24.10673598Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.10673598, -24.10673598}
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