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Simplifying 2x[(8 + -3) + 6x(2)] + -3 = 0 Combine like terms: 8 + -3 = 5 2x[(5) + 6x(2)] + -3 = 0 2x[5 + 6x(2)] + -3 = 0 Reorder the terms for easier multiplication: 2x[5 + 6 * 2x] + -3 = 0 Multiply 6 * 2 2x[5 + 12x] + -3 = 0 [5 * 2x + 12x * 2x] + -3 = 0 [10x + 24x2] + -3 = 0 Reorder the terms: -3 + 10x + 24x2 = 0 Solving -3 + 10x + 24x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -0.125 + 0.4166666667x + x2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + 0.4166666667x + 0.125 + x2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + 0.4166666667x + x2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + 0.4166666667x + x2 = 0 + 0.125 0.4166666667x + x2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 0.4166666667x + x2 = 0.125 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 = 0.125 + 0.04340277781 Reorder the terms: 0.04340277781 + 0.4166666667x + x2 = 0.125 + 0.04340277781 Combine like terms: 0.125 + 0.04340277781 = 0.16840277781 0.04340277781 + 0.4166666667x + x2 = 0.16840277781 Factor a perfect square on the left side: (x + 0.2083333334)(x + 0.2083333334) = 0.16840277781 Calculate the square root of the right side: 0.410369075 Break this problem into two subproblems by setting (x + 0.2083333334) equal to 0.410369075 and -0.410369075.Subproblem 1
x + 0.2083333334 = 0.410369075 Simplifying x + 0.2083333334 = 0.410369075 Reorder the terms: 0.2083333334 + x = 0.410369075 Solving 0.2083333334 + x = 0.410369075 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 = 0.410369075 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + x = 0.410369075 + -0.2083333334 x = 0.410369075 + -0.2083333334 Combine like terms: 0.410369075 + -0.2083333334 = 0.2020357416 x = 0.2020357416 Simplifying x = 0.2020357416Subproblem 2
x + 0.2083333334 = -0.410369075 Simplifying x + 0.2083333334 = -0.410369075 Reorder the terms: 0.2083333334 + x = -0.410369075 Solving 0.2083333334 + x = -0.410369075 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 = -0.410369075 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + x = -0.410369075 + -0.2083333334 x = -0.410369075 + -0.2083333334 Combine like terms: -0.410369075 + -0.2083333334 = -0.6187024084 x = -0.6187024084 Simplifying x = -0.6187024084Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2020357416, -0.6187024084}
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