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Simplifying x2 + 131x + -5775 = 0 Reorder the terms: -5775 + 131x + x2 = 0 Solving -5775 + 131x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '5775' to each side of the equation. -5775 + 131x + 5775 + x2 = 0 + 5775 Reorder the terms: -5775 + 5775 + 131x + x2 = 0 + 5775 Combine like terms: -5775 + 5775 = 0 0 + 131x + x2 = 0 + 5775 131x + x2 = 0 + 5775 Combine like terms: 0 + 5775 = 5775 131x + x2 = 5775 The x term is 131x. Take half its coefficient (65.5). Square it (4290.25) and add it to both sides. Add '4290.25' to each side of the equation. 131x + 4290.25 + x2 = 5775 + 4290.25 Reorder the terms: 4290.25 + 131x + x2 = 5775 + 4290.25 Combine like terms: 5775 + 4290.25 = 10065.25 4290.25 + 131x + x2 = 10065.25 Factor a perfect square on the left side: (x + 65.5)(x + 65.5) = 10065.25 Calculate the square root of the right side: 100.325719534 Break this problem into two subproblems by setting (x + 65.5) equal to 100.325719534 and -100.325719534.Subproblem 1
x + 65.5 = 100.325719534 Simplifying x + 65.5 = 100.325719534 Reorder the terms: 65.5 + x = 100.325719534 Solving 65.5 + x = 100.325719534 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-65.5' to each side of the equation. 65.5 + -65.5 + x = 100.325719534 + -65.5 Combine like terms: 65.5 + -65.5 = 0.0 0.0 + x = 100.325719534 + -65.5 x = 100.325719534 + -65.5 Combine like terms: 100.325719534 + -65.5 = 34.825719534 x = 34.825719534 Simplifying x = 34.825719534Subproblem 2
x + 65.5 = -100.325719534 Simplifying x + 65.5 = -100.325719534 Reorder the terms: 65.5 + x = -100.325719534 Solving 65.5 + x = -100.325719534 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-65.5' to each side of the equation. 65.5 + -65.5 + x = -100.325719534 + -65.5 Combine like terms: 65.5 + -65.5 = 0.0 0.0 + x = -100.325719534 + -65.5 x = -100.325719534 + -65.5 Combine like terms: -100.325719534 + -65.5 = -165.825719534 x = -165.825719534 Simplifying x = -165.825719534Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.825719534, -165.825719534}
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