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Simplifying x2 + -19x + -77 = 0 Reorder the terms: -77 + -19x + x2 = 0 Solving -77 + -19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '77' to each side of the equation. -77 + -19x + 77 + x2 = 0 + 77 Reorder the terms: -77 + 77 + -19x + x2 = 0 + 77 Combine like terms: -77 + 77 = 0 0 + -19x + x2 = 0 + 77 -19x + x2 = 0 + 77 Combine like terms: 0 + 77 = 77 -19x + x2 = 77 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 = 77 + 90.25 Reorder the terms: 90.25 + -19x + x2 = 77 + 90.25 Combine like terms: 77 + 90.25 = 167.25 90.25 + -19x + x2 = 167.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 167.25 Calculate the square root of the right side: 12.932517156 Break this problem into two subproblems by setting (x + -9.5) equal to 12.932517156 and -12.932517156.Subproblem 1
x + -9.5 = 12.932517156 Simplifying x + -9.5 = 12.932517156 Reorder the terms: -9.5 + x = 12.932517156 Solving -9.5 + x = 12.932517156 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 = 12.932517156 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 12.932517156 + 9.5 x = 12.932517156 + 9.5 Combine like terms: 12.932517156 + 9.5 = 22.432517156 x = 22.432517156 Simplifying x = 22.432517156Subproblem 2
x + -9.5 = -12.932517156 Simplifying x + -9.5 = -12.932517156 Reorder the terms: -9.5 + x = -12.932517156 Solving -9.5 + x = -12.932517156 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 = -12.932517156 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -12.932517156 + 9.5 x = -12.932517156 + 9.5 Combine like terms: -12.932517156 + 9.5 = -3.432517156 x = -3.432517156 Simplifying x = -3.432517156Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.432517156, -3.432517156}
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