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Simplifying (0.3 + 2x)(1 + 2x) = 8.173 Multiply (0.3 + 2x) * (1 + 2x) (0.3(1 + 2x) + 2x * (1 + 2x)) = 8.173 ((1 * 0.3 + 2x * 0.3) + 2x * (1 + 2x)) = 8.173 ((0.3 + 0.6x) + 2x * (1 + 2x)) = 8.173 (0.3 + 0.6x + (1 * 2x + 2x * 2x)) = 8.173 (0.3 + 0.6x + (2x + 4x2)) = 8.173 Combine like terms: 0.6x + 2x = 2.6x (0.3 + 2.6x + 4x2) = 8.173 Solving 0.3 + 2.6x + 4x2 = 8.173 Solving for variable 'x'. Reorder the terms: 0.3 + -8.173 + 2.6x + 4x2 = 8.173 + -8.173 Combine like terms: 0.3 + -8.173 = -7.873 -7.873 + 2.6x + 4x2 = 8.173 + -8.173 Combine like terms: 8.173 + -8.173 = 0.000 -7.873 + 2.6x + 4x2 = 0.000 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.96825 + 0.65x + x2 = 0.000 Move the constant term to the right: Add '1.96825' to each side of the equation. -1.96825 + 0.65x + 1.96825 + x2 = 0.000 + 1.96825 Reorder the terms: -1.96825 + 1.96825 + 0.65x + x2 = 0.000 + 1.96825 Combine like terms: -1.96825 + 1.96825 = 0.00000 0.00000 + 0.65x + x2 = 0.000 + 1.96825 0.65x + x2 = 0.000 + 1.96825 Combine like terms: 0.000 + 1.96825 = 1.96825 0.65x + x2 = 1.96825 The x term is 0.65x. Take half its coefficient (0.325). Square it (0.105625) and add it to both sides. Add '0.105625' to each side of the equation. 0.65x + 0.105625 + x2 = 1.96825 + 0.105625 Reorder the terms: 0.105625 + 0.65x + x2 = 1.96825 + 0.105625 Combine like terms: 1.96825 + 0.105625 = 2.073875 0.105625 + 0.65x + x2 = 2.073875 Factor a perfect square on the left side: (x + 0.325)(x + 0.325) = 2.073875 Calculate the square root of the right side: 1.440095483 Break this problem into two subproblems by setting (x + 0.325) equal to 1.440095483 and -1.440095483.Subproblem 1
x + 0.325 = 1.440095483 Simplifying x + 0.325 = 1.440095483 Reorder the terms: 0.325 + x = 1.440095483 Solving 0.325 + x = 1.440095483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.325' to each side of the equation. 0.325 + -0.325 + x = 1.440095483 + -0.325 Combine like terms: 0.325 + -0.325 = 0.000 0.000 + x = 1.440095483 + -0.325 x = 1.440095483 + -0.325 Combine like terms: 1.440095483 + -0.325 = 1.115095483 x = 1.115095483 Simplifying x = 1.115095483Subproblem 2
x + 0.325 = -1.440095483 Simplifying x + 0.325 = -1.440095483 Reorder the terms: 0.325 + x = -1.440095483 Solving 0.325 + x = -1.440095483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.325' to each side of the equation. 0.325 + -0.325 + x = -1.440095483 + -0.325 Combine like terms: 0.325 + -0.325 = 0.000 0.000 + x = -1.440095483 + -0.325 x = -1.440095483 + -0.325 Combine like terms: -1.440095483 + -0.325 = -1.765095483 x = -1.765095483 Simplifying x = -1.765095483Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.115095483, -1.765095483}
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