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Simplifying x2 + -19x + -71 = 0 Reorder the terms: -71 + -19x + x2 = 0 Solving -71 + -19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '71' to each side of the equation. -71 + -19x + 71 + x2 = 0 + 71 Reorder the terms: -71 + 71 + -19x + x2 = 0 + 71 Combine like terms: -71 + 71 = 0 0 + -19x + x2 = 0 + 71 -19x + x2 = 0 + 71 Combine like terms: 0 + 71 = 71 -19x + x2 = 71 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = 71 + 90.25 Reorder the terms: 90.25 + -19x + x2 = 71 + 90.25 Combine like terms: 71 + 90.25 = 161.25 90.25 + -19x + x2 = 161.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 161.25 Calculate the square root of the right side: 12.698425099 Break this problem into two subproblems by setting (x + -9.5) equal to 12.698425099 and -12.698425099.Subproblem 1
x + -9.5 = 12.698425099 Simplifying x + -9.5 = 12.698425099 Reorder the terms: -9.5 + x = 12.698425099 Solving -9.5 + x = 12.698425099 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 12.698425099 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 12.698425099 + 9.5 x = 12.698425099 + 9.5 Combine like terms: 12.698425099 + 9.5 = 22.198425099 x = 22.198425099 Simplifying x = 22.198425099Subproblem 2
x + -9.5 = -12.698425099 Simplifying x + -9.5 = -12.698425099 Reorder the terms: -9.5 + x = -12.698425099 Solving -9.5 + x = -12.698425099 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -12.698425099 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -12.698425099 + 9.5 x = -12.698425099 + 9.5 Combine like terms: -12.698425099 + 9.5 = -3.198425099 x = -3.198425099 Simplifying x = -3.198425099Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.198425099, -3.198425099}
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