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Simplifying x2 + -20x + -98 = 0 Reorder the terms: -98 + -20x + x2 = 0 Solving -98 + -20x + x2 = 0 Solving for variable 'x'. 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 = 24.071247279 x = 24.071247279 Simplifying x = 24.071247279Subproblem 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 = -4.071247279 x = -4.071247279 Simplifying x = -4.071247279Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.071247279, -4.071247279}
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