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Simplifying 4x(4 + 6x) = 8 + -5 (4 * 4x + 6x * 4x) = 8 + -5 (16x + 24x2) = 8 + -5 Combine like terms: 8 + -5 = 3 16x + 24x2 = 3 Solving 16x + 24x2 = 3 Solving for variable 'x'. Reorder the terms: -3 + 16x + 24x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 16x + 24x2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -0.125 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + 0.6666666667x + 0.125 + x2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + 0.6666666667x + x2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + 0.6666666667x + x2 = 0 + 0.125 0.6666666667x + x2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 0.6666666667x + x2 = 0.125 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 0.125 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 0.125 + 0.1111111112 Combine like terms: 0.125 + 0.1111111112 = 0.2361111112 0.1111111112 + 0.6666666667x + x2 = 0.2361111112 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 0.2361111112 Calculate the square root of the right side: 0.485912658 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 0.485912658 and -0.485912658.Subproblem 1
x + 0.3333333334 = 0.485912658 Simplifying x + 0.3333333334 = 0.485912658 Reorder the terms: 0.3333333334 + x = 0.485912658 Solving 0.3333333334 + x = 0.485912658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 0.485912658 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 0.485912658 + -0.3333333334 x = 0.485912658 + -0.3333333334 Combine like terms: 0.485912658 + -0.3333333334 = 0.1525793246 x = 0.1525793246 Simplifying x = 0.1525793246Subproblem 2
x + 0.3333333334 = -0.485912658 Simplifying x + 0.3333333334 = -0.485912658 Reorder the terms: 0.3333333334 + x = -0.485912658 Solving 0.3333333334 + x = -0.485912658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -0.485912658 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -0.485912658 + -0.3333333334 x = -0.485912658 + -0.3333333334 Combine like terms: -0.485912658 + -0.3333333334 = -0.8192459914 x = -0.8192459914 Simplifying x = -0.8192459914Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1525793246, -0.8192459914}
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