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Simplifying 7x2 + -24 = 6x + -5x Reorder the terms: -24 + 7x2 = 6x + -5x Combine like terms: 6x + -5x = 1x -24 + 7x2 = 1x Solving -24 + 7x2 = 1x Solving for variable 'x'. Reorder the terms: -24 + -1x + 7x2 = 1x + -1x Combine like terms: 1x + -1x = 0 -24 + -1x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -3.428571429 + -0.1428571429x + x2 = 0 Move the constant term to the right: Add '3.428571429' to each side of the equation. -3.428571429 + -0.1428571429x + 3.428571429 + x2 = 0 + 3.428571429 Reorder the terms: -3.428571429 + 3.428571429 + -0.1428571429x + x2 = 0 + 3.428571429 Combine like terms: -3.428571429 + 3.428571429 = 0.000000000 0.000000000 + -0.1428571429x + x2 = 0 + 3.428571429 -0.1428571429x + x2 = 0 + 3.428571429 Combine like terms: 0 + 3.428571429 = 3.428571429 -0.1428571429x + x2 = 3.428571429 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 = 3.428571429 + 0.005102040819 Reorder the terms: 0.005102040819 + -0.1428571429x + x2 = 3.428571429 + 0.005102040819 Combine like terms: 3.428571429 + 0.005102040819 = 3.433673469819 0.005102040819 + -0.1428571429x + x2 = 3.433673469819 Factor a perfect square on the left side: (x + -0.07142857145)(x + -0.07142857145) = 3.433673469819 Calculate the square root of the right side: 1.853017396 Break this problem into two subproblems by setting (x + -0.07142857145) equal to 1.853017396 and -1.853017396.Subproblem 1
x + -0.07142857145 = 1.853017396 Simplifying x + -0.07142857145 = 1.853017396 Reorder the terms: -0.07142857145 + x = 1.853017396 Solving -0.07142857145 + x = 1.853017396 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 = 1.853017396 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = 1.853017396 + 0.07142857145 x = 1.853017396 + 0.07142857145 Combine like terms: 1.853017396 + 0.07142857145 = 1.92444596745 x = 1.92444596745 Simplifying x = 1.92444596745Subproblem 2
x + -0.07142857145 = -1.853017396 Simplifying x + -0.07142857145 = -1.853017396 Reorder the terms: -0.07142857145 + x = -1.853017396 Solving -0.07142857145 + x = -1.853017396 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 = -1.853017396 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = -1.853017396 + 0.07142857145 x = -1.853017396 + 0.07142857145 Combine like terms: -1.853017396 + 0.07142857145 = -1.78158882455 x = -1.78158882455 Simplifying x = -1.78158882455Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.92444596745, -1.78158882455}
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