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Simplifying 4x + 7 = 14x2 + 6x + -4 Reorder the terms: 7 + 4x = 14x2 + 6x + -4 Reorder the terms: 7 + 4x = -4 + 6x + 14x2 Solving 7 + 4x = -4 + 6x + 14x2 Solving for variable 'x'. Reorder the terms: 7 + 4 + 4x + -6x + -14x2 = -4 + 6x + 14x2 + 4 + -6x + -14x2 Combine like terms: 7 + 4 = 11 11 + 4x + -6x + -14x2 = -4 + 6x + 14x2 + 4 + -6x + -14x2 Combine like terms: 4x + -6x = -2x 11 + -2x + -14x2 = -4 + 6x + 14x2 + 4 + -6x + -14x2 Reorder the terms: 11 + -2x + -14x2 = -4 + 4 + 6x + -6x + 14x2 + -14x2 Combine like terms: -4 + 4 = 0 11 + -2x + -14x2 = 0 + 6x + -6x + 14x2 + -14x2 11 + -2x + -14x2 = 6x + -6x + 14x2 + -14x2 Combine like terms: 6x + -6x = 0 11 + -2x + -14x2 = 0 + 14x2 + -14x2 11 + -2x + -14x2 = 14x2 + -14x2 Combine like terms: 14x2 + -14x2 = 0 11 + -2x + -14x2 = 0 Begin completing the square. Divide all terms by -14 the coefficient of the squared term: Divide each side by '-14'. -0.7857142857 + 0.1428571429x + x2 = 0 Move the constant term to the right: Add '0.7857142857' to each side of the equation. -0.7857142857 + 0.1428571429x + 0.7857142857 + x2 = 0 + 0.7857142857 Reorder the terms: -0.7857142857 + 0.7857142857 + 0.1428571429x + x2 = 0 + 0.7857142857 Combine like terms: -0.7857142857 + 0.7857142857 = 0.0000000000 0.0000000000 + 0.1428571429x + x2 = 0 + 0.7857142857 0.1428571429x + x2 = 0 + 0.7857142857 Combine like terms: 0 + 0.7857142857 = 0.7857142857 0.1428571429x + x2 = 0.7857142857 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 = 0.7857142857 + 0.005102040819 Reorder the terms: 0.005102040819 + 0.1428571429x + x2 = 0.7857142857 + 0.005102040819 Combine like terms: 0.7857142857 + 0.005102040819 = 0.790816326519 0.005102040819 + 0.1428571429x + x2 = 0.790816326519 Factor a perfect square on the left side: (x + 0.07142857145)(x + 0.07142857145) = 0.790816326519 Calculate the square root of the right side: 0.889278543 Break this problem into two subproblems by setting (x + 0.07142857145) equal to 0.889278543 and -0.889278543.Subproblem 1
x + 0.07142857145 = 0.889278543 Simplifying x + 0.07142857145 = 0.889278543 Reorder the terms: 0.07142857145 + x = 0.889278543 Solving 0.07142857145 + x = 0.889278543 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 = 0.889278543 + -0.07142857145 Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000 0.00000000000 + x = 0.889278543 + -0.07142857145 x = 0.889278543 + -0.07142857145 Combine like terms: 0.889278543 + -0.07142857145 = 0.81784997155 x = 0.81784997155 Simplifying x = 0.81784997155Subproblem 2
x + 0.07142857145 = -0.889278543 Simplifying x + 0.07142857145 = -0.889278543 Reorder the terms: 0.07142857145 + x = -0.889278543 Solving 0.07142857145 + x = -0.889278543 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 = -0.889278543 + -0.07142857145 Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000 0.00000000000 + x = -0.889278543 + -0.07142857145 x = -0.889278543 + -0.07142857145 Combine like terms: -0.889278543 + -0.07142857145 = -0.96070711445 x = -0.96070711445 Simplifying x = -0.96070711445Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.81784997155, -0.96070711445}
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