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Simplifying x2 + -19x + -84 = 0 Reorder the terms: -84 + -19x + x2 = 0 Solving -84 + -19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '84' to each side of the equation. -84 + -19x + 84 + x2 = 0 + 84 Reorder the terms: -84 + 84 + -19x + x2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + -19x + x2 = 0 + 84 -19x + x2 = 0 + 84 Combine like terms: 0 + 84 = 84 -19x + x2 = 84 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 = 84 + 90.25 Reorder the terms: 90.25 + -19x + x2 = 84 + 90.25 Combine like terms: 84 + 90.25 = 174.25 90.25 + -19x + x2 = 174.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 174.25 Calculate the square root of the right side: 13.200378782 Break this problem into two subproblems by setting (x + -9.5) equal to 13.200378782 and -13.200378782.Subproblem 1
x + -9.5 = 13.200378782 Simplifying x + -9.5 = 13.200378782 Reorder the terms: -9.5 + x = 13.200378782 Solving -9.5 + x = 13.200378782 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 = 13.200378782 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 13.200378782 + 9.5 x = 13.200378782 + 9.5 Combine like terms: 13.200378782 + 9.5 = 22.700378782 x = 22.700378782 Simplifying x = 22.700378782Subproblem 2
x + -9.5 = -13.200378782 Simplifying x + -9.5 = -13.200378782 Reorder the terms: -9.5 + x = -13.200378782 Solving -9.5 + x = -13.200378782 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 = -13.200378782 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -13.200378782 + 9.5 x = -13.200378782 + 9.5 Combine like terms: -13.200378782 + 9.5 = -3.700378782 x = -3.700378782 Simplifying x = -3.700378782Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.700378782, -3.700378782}
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