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Simplifying 38.1x2 + 2.72x + -0.065 = 0 Reorder the terms: -0.065 + 2.72x + 38.1x2 = 0 Solving -0.065 + 2.72x + 38.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 38.1 the coefficient of the squared term: Divide each side by '38.1'. -0.001706036745 + 0.07139107612x + x2 = 0 Move the constant term to the right: Add '0.001706036745' to each side of the equation. -0.001706036745 + 0.07139107612x + 0.001706036745 + x2 = 0 + 0.001706036745 Reorder the terms: -0.001706036745 + 0.001706036745 + 0.07139107612x + x2 = 0 + 0.001706036745 Combine like terms: -0.001706036745 + 0.001706036745 = 0.000000000000 0.000000000000 + 0.07139107612x + x2 = 0 + 0.001706036745 0.07139107612x + x2 = 0 + 0.001706036745 Combine like terms: 0 + 0.001706036745 = 0.001706036745 0.07139107612x + x2 = 0.001706036745 The x term is 0.07139107612x. Take half its coefficient (0.03569553806). Square it (0.001274171437) and add it to both sides. Add '0.001274171437' to each side of the equation. 0.07139107612x + 0.001274171437 + x2 = 0.001706036745 + 0.001274171437 Reorder the terms: 0.001274171437 + 0.07139107612x + x2 = 0.001706036745 + 0.001274171437 Combine like terms: 0.001706036745 + 0.001274171437 = 0.002980208182 0.001274171437 + 0.07139107612x + x2 = 0.002980208182 Factor a perfect square on the left side: (x + 0.03569553806)(x + 0.03569553806) = 0.002980208182 Calculate the square root of the right side: 0.054591283 Break this problem into two subproblems by setting (x + 0.03569553806) equal to 0.054591283 and -0.054591283.Subproblem 1
x + 0.03569553806 = 0.054591283 Simplifying x + 0.03569553806 = 0.054591283 Reorder the terms: 0.03569553806 + x = 0.054591283 Solving 0.03569553806 + x = 0.054591283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03569553806' to each side of the equation. 0.03569553806 + -0.03569553806 + x = 0.054591283 + -0.03569553806 Combine like terms: 0.03569553806 + -0.03569553806 = 0.00000000000 0.00000000000 + x = 0.054591283 + -0.03569553806 x = 0.054591283 + -0.03569553806 Combine like terms: 0.054591283 + -0.03569553806 = 0.01889574494 x = 0.01889574494 Simplifying x = 0.01889574494Subproblem 2
x + 0.03569553806 = -0.054591283 Simplifying x + 0.03569553806 = -0.054591283 Reorder the terms: 0.03569553806 + x = -0.054591283 Solving 0.03569553806 + x = -0.054591283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03569553806' to each side of the equation. 0.03569553806 + -0.03569553806 + x = -0.054591283 + -0.03569553806 Combine like terms: 0.03569553806 + -0.03569553806 = 0.00000000000 0.00000000000 + x = -0.054591283 + -0.03569553806 x = -0.054591283 + -0.03569553806 Combine like terms: -0.054591283 + -0.03569553806 = -0.09028682106 x = -0.09028682106 Simplifying x = -0.09028682106Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.01889574494, -0.09028682106}
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