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Simplifying 7x2 + -1x + -52 = 0 Reorder the terms: -52 + -1x + 7x2 = 0 Solving -52 + -1x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -7.428571429 + -0.1428571429x + x2 = 0 Move the constant term to the right: Add '7.428571429' to each side of the equation. -7.428571429 + -0.1428571429x + 7.428571429 + x2 = 0 + 7.428571429 Reorder the terms: -7.428571429 + 7.428571429 + -0.1428571429x + x2 = 0 + 7.428571429 Combine like terms: -7.428571429 + 7.428571429 = 0.000000000 0.000000000 + -0.1428571429x + x2 = 0 + 7.428571429 -0.1428571429x + x2 = 0 + 7.428571429 Combine like terms: 0 + 7.428571429 = 7.428571429 -0.1428571429x + x2 = 7.428571429 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 = 7.428571429 + 0.005102040819 Reorder the terms: 0.005102040819 + -0.1428571429x + x2 = 7.428571429 + 0.005102040819 Combine like terms: 7.428571429 + 0.005102040819 = 7.433673469819 0.005102040819 + -0.1428571429x + x2 = 7.433673469819 Factor a perfect square on the left side: (x + -0.07142857145)(x + -0.07142857145) = 7.433673469819 Calculate the square root of the right side: 2.726476384 Break this problem into two subproblems by setting (x + -0.07142857145) equal to 2.726476384 and -2.726476384.Subproblem 1
x + -0.07142857145 = 2.726476384 Simplifying x + -0.07142857145 = 2.726476384 Reorder the terms: -0.07142857145 + x = 2.726476384 Solving -0.07142857145 + x = 2.726476384 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 = 2.726476384 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = 2.726476384 + 0.07142857145 x = 2.726476384 + 0.07142857145 Combine like terms: 2.726476384 + 0.07142857145 = 2.79790495545 x = 2.79790495545 Simplifying x = 2.79790495545Subproblem 2
x + -0.07142857145 = -2.726476384 Simplifying x + -0.07142857145 = -2.726476384 Reorder the terms: -0.07142857145 + x = -2.726476384 Solving -0.07142857145 + x = -2.726476384 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 = -2.726476384 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = -2.726476384 + 0.07142857145 x = -2.726476384 + 0.07142857145 Combine like terms: -2.726476384 + 0.07142857145 = -2.65504781255 x = -2.65504781255 Simplifying x = -2.65504781255Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.79790495545, -2.65504781255}
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