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Simplifying 7x2 + -1x + -80 = 87.2 Reorder the terms: -80 + -1x + 7x2 = 87.2 Solving -80 + -1x + 7x2 = 87.2 Solving for variable 'x'. Reorder the terms: -80 + -87.2 + -1x + 7x2 = 87.2 + -87.2 Combine like terms: -80 + -87.2 = -167.2 -167.2 + -1x + 7x2 = 87.2 + -87.2 Combine like terms: 87.2 + -87.2 = 0.0 -167.2 + -1x + 7x2 = 0.0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -23.88571429 + -0.1428571429x + x2 = 0.0 Move the constant term to the right: Add '23.88571429' to each side of the equation. -23.88571429 + -0.1428571429x + 23.88571429 + x2 = 0.0 + 23.88571429 Reorder the terms: -23.88571429 + 23.88571429 + -0.1428571429x + x2 = 0.0 + 23.88571429 Combine like terms: -23.88571429 + 23.88571429 = 0.00000000 0.00000000 + -0.1428571429x + x2 = 0.0 + 23.88571429 -0.1428571429x + x2 = 0.0 + 23.88571429 Combine like terms: 0.0 + 23.88571429 = 23.88571429 -0.1428571429x + x2 = 23.88571429 The x term is -0.1428571429x. Take half its coefficient (-0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. -0.1428571429x + 0.005102040819 + x2 = 23.88571429 + 0.005102040819 Reorder the terms: 0.005102040819 + -0.1428571429x + x2 = 23.88571429 + 0.005102040819 Combine like terms: 23.88571429 + 0.005102040819 = 23.890816330819 0.005102040819 + -0.1428571429x + x2 = 23.890816330819 Factor a perfect square on the left side: (x + -0.07142857145)(x + -0.07142857145) = 23.890816330819 Calculate the square root of the right side: 4.887823271 Break this problem into two subproblems by setting (x + -0.07142857145) equal to 4.887823271 and -4.887823271.Subproblem 1
x + -0.07142857145 = 4.887823271 Simplifying x + -0.07142857145 = 4.887823271 Reorder the terms: -0.07142857145 + x = 4.887823271 Solving -0.07142857145 + x = 4.887823271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + x = 4.887823271 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = 4.887823271 + 0.07142857145 x = 4.887823271 + 0.07142857145 Combine like terms: 4.887823271 + 0.07142857145 = 4.95925184245 x = 4.95925184245 Simplifying x = 4.95925184245Subproblem 2
x + -0.07142857145 = -4.887823271 Simplifying x + -0.07142857145 = -4.887823271 Reorder the terms: -0.07142857145 + x = -4.887823271 Solving -0.07142857145 + x = -4.887823271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + x = -4.887823271 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = -4.887823271 + 0.07142857145 x = -4.887823271 + 0.07142857145 Combine like terms: -4.887823271 + 0.07142857145 = -4.81639469955 x = -4.81639469955 Simplifying x = -4.81639469955Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.95925184245, -4.81639469955}
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