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Simplifying 7x2 + -1x = 46 Reorder the terms: -1x + 7x2 = 46 Solving -1x + 7x2 = 46 Solving for variable 'x'. Reorder the terms: -46 + -1x + 7x2 = 46 + -46 Combine like terms: 46 + -46 = 0 -46 + -1x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -6.571428571 + -0.1428571429x + x2 = 0 Move the constant term to the right: Add '6.571428571' to each side of the equation. -6.571428571 + -0.1428571429x + 6.571428571 + x2 = 0 + 6.571428571 Reorder the terms: -6.571428571 + 6.571428571 + -0.1428571429x + x2 = 0 + 6.571428571 Combine like terms: -6.571428571 + 6.571428571 = 0.000000000 0.000000000 + -0.1428571429x + x2 = 0 + 6.571428571 -0.1428571429x + x2 = 0 + 6.571428571 Combine like terms: 0 + 6.571428571 = 6.571428571 -0.1428571429x + x2 = 6.571428571 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 = 6.571428571 + 0.005102040819 Reorder the terms: 0.005102040819 + -0.1428571429x + x2 = 6.571428571 + 0.005102040819 Combine like terms: 6.571428571 + 0.005102040819 = 6.576530611819 0.005102040819 + -0.1428571429x + x2 = 6.576530611819 Factor a perfect square on the left side: (x + -0.07142857145)(x + -0.07142857145) = 6.576530611819 Calculate the square root of the right side: 2.564474724 Break this problem into two subproblems by setting (x + -0.07142857145) equal to 2.564474724 and -2.564474724.Subproblem 1
x + -0.07142857145 = 2.564474724 Simplifying x + -0.07142857145 = 2.564474724 Reorder the terms: -0.07142857145 + x = 2.564474724 Solving -0.07142857145 + x = 2.564474724 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 = 2.564474724 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = 2.564474724 + 0.07142857145 x = 2.564474724 + 0.07142857145 Combine like terms: 2.564474724 + 0.07142857145 = 2.63590329545 x = 2.63590329545 Simplifying x = 2.63590329545Subproblem 2
x + -0.07142857145 = -2.564474724 Simplifying x + -0.07142857145 = -2.564474724 Reorder the terms: -0.07142857145 + x = -2.564474724 Solving -0.07142857145 + x = -2.564474724 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 = -2.564474724 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = -2.564474724 + 0.07142857145 x = -2.564474724 + 0.07142857145 Combine like terms: -2.564474724 + 0.07142857145 = -2.49304615255 x = -2.49304615255 Simplifying x = -2.49304615255Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.63590329545, -2.49304615255}
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