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Simplifying 72x2 + -4x2 + 2x + 8 = 0 Reorder the terms: 8 + 2x + 72x2 + -4x2 = 0 Combine like terms: 72x2 + -4x2 = 68x2 8 + 2x + 68x2 = 0 Solving 8 + 2x + 68x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + x + 34x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + x + 34x2)' equal to zero and attempt to solve: Simplifying 4 + x + 34x2 = 0 Solving 4 + x + 34x2 = 0 Begin completing the square. Divide all terms by 34 the coefficient of the squared term: Divide each side by '34'. 0.1176470588 + 0.02941176471x + x2 = 0 Move the constant term to the right: Add '-0.1176470588' to each side of the equation. 0.1176470588 + 0.02941176471x + -0.1176470588 + x2 = 0 + -0.1176470588 Reorder the terms: 0.1176470588 + -0.1176470588 + 0.02941176471x + x2 = 0 + -0.1176470588 Combine like terms: 0.1176470588 + -0.1176470588 = 0.0000000000 0.0000000000 + 0.02941176471x + x2 = 0 + -0.1176470588 0.02941176471x + x2 = 0 + -0.1176470588 Combine like terms: 0 + -0.1176470588 = -0.1176470588 0.02941176471x + x2 = -0.1176470588 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.02941176471x + 0.25 + x2 = -0.1176470588 + 0.25 Reorder the terms: 0.25 + 0.02941176471x + x2 = -0.1176470588 + 0.25 Combine like terms: -0.1176470588 + 0.25 = 0.1323529412 0.25 + 0.02941176471x + x2 = 0.1323529412 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.1323529412 Calculate the square root of the right side: 0.363803438 Break this problem into two subproblems by setting (x + 0.5) equal to 0.363803438 and -0.363803438.Subproblem 1
x + 0.5 = 0.363803438 Simplifying x + 0.5 = 0.363803438 Reorder the terms: 0.5 + x = 0.363803438 Solving 0.5 + x = 0.363803438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.363803438 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.363803438 + -0.5 x = 0.363803438 + -0.5 Combine like terms: 0.363803438 + -0.5 = -0.136196562 x = -0.136196562 Simplifying x = -0.136196562Subproblem 2
x + 0.5 = -0.363803438 Simplifying x + 0.5 = -0.363803438 Reorder the terms: 0.5 + x = -0.363803438 Solving 0.5 + x = -0.363803438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.363803438 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.363803438 + -0.5 x = -0.363803438 + -0.5 Combine like terms: -0.363803438 + -0.5 = -0.863803438 x = -0.863803438 Simplifying x = -0.863803438Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.136196562, -0.863803438}Solution
x = {-0.136196562, -0.863803438}
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