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Simplifying 8(2x + 1) * 3x + 4 = 4x + 3 Reorder the terms: 8(1 + 2x) * 3x + 4 = 4x + 3 Reorder the terms for easier multiplication: 8 * 3x(1 + 2x) + 4 = 4x + 3 Multiply 8 * 3 24x(1 + 2x) + 4 = 4x + 3 (1 * 24x + 2x * 24x) + 4 = 4x + 3 (24x + 48x2) + 4 = 4x + 3 Reorder the terms: 4 + 24x + 48x2 = 4x + 3 Reorder the terms: 4 + 24x + 48x2 = 3 + 4x Solving 4 + 24x + 48x2 = 3 + 4x Solving for variable 'x'. Reorder the terms: 4 + -3 + 24x + -4x + 48x2 = 3 + 4x + -3 + -4x Combine like terms: 4 + -3 = 1 1 + 24x + -4x + 48x2 = 3 + 4x + -3 + -4x Combine like terms: 24x + -4x = 20x 1 + 20x + 48x2 = 3 + 4x + -3 + -4x Reorder the terms: 1 + 20x + 48x2 = 3 + -3 + 4x + -4x Combine like terms: 3 + -3 = 0 1 + 20x + 48x2 = 0 + 4x + -4x 1 + 20x + 48x2 = 4x + -4x Combine like terms: 4x + -4x = 0 1 + 20x + 48x2 = 0 Begin completing the square. Divide all terms by 48 the coefficient of the squared term: Divide each side by '48'. 0.02083333333 + 0.4166666667x + x2 = 0 Move the constant term to the right: Add '-0.02083333333' to each side of the equation. 0.02083333333 + 0.4166666667x + -0.02083333333 + x2 = 0 + -0.02083333333 Reorder the terms: 0.02083333333 + -0.02083333333 + 0.4166666667x + x2 = 0 + -0.02083333333 Combine like terms: 0.02083333333 + -0.02083333333 = 0.00000000000 0.00000000000 + 0.4166666667x + x2 = 0 + -0.02083333333 0.4166666667x + x2 = 0 + -0.02083333333 Combine like terms: 0 + -0.02083333333 = -0.02083333333 0.4166666667x + x2 = -0.02083333333 The x term is 0.4166666667x. Take half its coefficient (0.2083333334). Square it (0.04340277781) and add it to both sides. Add '0.04340277781' to each side of the equation. 0.4166666667x + 0.04340277781 + x2 = -0.02083333333 + 0.04340277781 Reorder the terms: 0.04340277781 + 0.4166666667x + x2 = -0.02083333333 + 0.04340277781 Combine like terms: -0.02083333333 + 0.04340277781 = 0.02256944448 0.04340277781 + 0.4166666667x + x2 = 0.02256944448 Factor a perfect square on the left side: (x + 0.2083333334)(x + 0.2083333334) = 0.02256944448 Calculate the square root of the right side: 0.150231303 Break this problem into two subproblems by setting (x + 0.2083333334) equal to 0.150231303 and -0.150231303.Subproblem 1
x + 0.2083333334 = 0.150231303 Simplifying x + 0.2083333334 = 0.150231303 Reorder the terms: 0.2083333334 + x = 0.150231303 Solving 0.2083333334 + x = 0.150231303 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2083333334' to each side of the equation. 0.2083333334 + -0.2083333334 + x = 0.150231303 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + x = 0.150231303 + -0.2083333334 x = 0.150231303 + -0.2083333334 Combine like terms: 0.150231303 + -0.2083333334 = -0.0581020304 x = -0.0581020304 Simplifying x = -0.0581020304Subproblem 2
x + 0.2083333334 = -0.150231303 Simplifying x + 0.2083333334 = -0.150231303 Reorder the terms: 0.2083333334 + x = -0.150231303 Solving 0.2083333334 + x = -0.150231303 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2083333334' to each side of the equation. 0.2083333334 + -0.2083333334 + x = -0.150231303 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + x = -0.150231303 + -0.2083333334 x = -0.150231303 + -0.2083333334 Combine like terms: -0.150231303 + -0.2083333334 = -0.3585646364 x = -0.3585646364 Simplifying x = -0.3585646364Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.0581020304, -0.3585646364}
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