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Simplifying x2 + 20x + -101 = -3 Reorder the terms: -101 + 20x + x2 = -3 Solving -101 + 20x + x2 = -3 Solving for variable 'x'. Reorder the terms: -101 + 3 + 20x + x2 = -3 + 3 Combine like terms: -101 + 3 = -98 -98 + 20x + x2 = -3 + 3 Combine like terms: -3 + 3 = 0 -98 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '98' to each side of the equation. -98 + 20x + 98 + x2 = 0 + 98 Reorder the terms: -98 + 98 + 20x + x2 = 0 + 98 Combine like terms: -98 + 98 = 0 0 + 20x + x2 = 0 + 98 20x + x2 = 0 + 98 Combine like terms: 0 + 98 = 98 20x + x2 = 98 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 = 98 + 100 Reorder the terms: 100 + 20x + x2 = 98 + 100 Combine like terms: 98 + 100 = 198 100 + 20x + x2 = 198 Factor a perfect square on the left side: (x + 10)(x + 10) = 198 Calculate the square root of the right side: 14.071247279 Break this problem into two subproblems by setting (x + 10) equal to 14.071247279 and -14.071247279.Subproblem 1
x + 10 = 14.071247279 Simplifying x + 10 = 14.071247279 Reorder the terms: 10 + x = 14.071247279 Solving 10 + x = 14.071247279 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 = 14.071247279 + -10 Combine like terms: 10 + -10 = 0 0 + x = 14.071247279 + -10 x = 14.071247279 + -10 Combine like terms: 14.071247279 + -10 = 4.071247279 x = 4.071247279 Simplifying x = 4.071247279Subproblem 2
x + 10 = -14.071247279 Simplifying x + 10 = -14.071247279 Reorder the terms: 10 + x = -14.071247279 Solving 10 + x = -14.071247279 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 = -14.071247279 + -10 Combine like terms: 10 + -10 = 0 0 + x = -14.071247279 + -10 x = -14.071247279 + -10 Combine like terms: -14.071247279 + -10 = -24.071247279 x = -24.071247279 Simplifying x = -24.071247279Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.071247279, -24.071247279}
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