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Simplifying 7x2 + -1x = 14 Reorder the terms: -1x + 7x2 = 14 Solving -1x + 7x2 = 14 Solving for variable 'x'. Reorder the terms: -14 + -1x + 7x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + -1x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2 + -0.1428571429x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.1428571429x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -0.1428571429x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.1428571429x + x2 = 0 + 2 -0.1428571429x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.1428571429x + x2 = 2 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 = 2 + 0.005102040819 Reorder the terms: 0.005102040819 + -0.1428571429x + x2 = 2 + 0.005102040819 Combine like terms: 2 + 0.005102040819 = 2.005102040819 0.005102040819 + -0.1428571429x + x2 = 2.005102040819 Factor a perfect square on the left side: (x + -0.07142857145)(x + -0.07142857145) = 2.005102040819 Calculate the square root of the right side: 1.416016257 Break this problem into two subproblems by setting (x + -0.07142857145) equal to 1.416016257 and -1.416016257.Subproblem 1
x + -0.07142857145 = 1.416016257 Simplifying x + -0.07142857145 = 1.416016257 Reorder the terms: -0.07142857145 + x = 1.416016257 Solving -0.07142857145 + x = 1.416016257 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 = 1.416016257 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = 1.416016257 + 0.07142857145 x = 1.416016257 + 0.07142857145 Combine like terms: 1.416016257 + 0.07142857145 = 1.48744482845 x = 1.48744482845 Simplifying x = 1.48744482845Subproblem 2
x + -0.07142857145 = -1.416016257 Simplifying x + -0.07142857145 = -1.416016257 Reorder the terms: -0.07142857145 + x = -1.416016257 Solving -0.07142857145 + x = -1.416016257 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 = -1.416016257 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = -1.416016257 + 0.07142857145 x = -1.416016257 + 0.07142857145 Combine like terms: -1.416016257 + 0.07142857145 = -1.34458768555 x = -1.34458768555 Simplifying x = -1.34458768555Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.48744482845, -1.34458768555}
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