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Simplifying 8(6x + 3) * x = 5 Reorder the terms: 8(3 + 6x) * x = 5 Reorder the terms for easier multiplication: 8x(3 + 6x) = 5 (3 * 8x + 6x * 8x) = 5 (24x + 48x2) = 5 Solving 24x + 48x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 24x + 48x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 24x + 48x2 = 0 Begin completing the square. Divide all terms by 48 the coefficient of the squared term: Divide each side by '48'. -0.1041666667 + 0.5x + x2 = 0 Move the constant term to the right: Add '0.1041666667' to each side of the equation. -0.1041666667 + 0.5x + 0.1041666667 + x2 = 0 + 0.1041666667 Reorder the terms: -0.1041666667 + 0.1041666667 + 0.5x + x2 = 0 + 0.1041666667 Combine like terms: -0.1041666667 + 0.1041666667 = 0.0000000000 0.0000000000 + 0.5x + x2 = 0 + 0.1041666667 0.5x + x2 = 0 + 0.1041666667 Combine like terms: 0 + 0.1041666667 = 0.1041666667 0.5x + x2 = 0.1041666667 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 0.1041666667 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 0.1041666667 + 0.0625 Combine like terms: 0.1041666667 + 0.0625 = 0.1666666667 0.0625 + 0.5x + x2 = 0.1666666667 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 0.1666666667 Calculate the square root of the right side: 0.408248291 Break this problem into two subproblems by setting (x + 0.25) equal to 0.408248291 and -0.408248291.Subproblem 1
x + 0.25 = 0.408248291 Simplifying x + 0.25 = 0.408248291 Reorder the terms: 0.25 + x = 0.408248291 Solving 0.25 + x = 0.408248291 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 0.408248291 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 0.408248291 + -0.25 x = 0.408248291 + -0.25 Combine like terms: 0.408248291 + -0.25 = 0.158248291 x = 0.158248291 Simplifying x = 0.158248291Subproblem 2
x + 0.25 = -0.408248291 Simplifying x + 0.25 = -0.408248291 Reorder the terms: 0.25 + x = -0.408248291 Solving 0.25 + x = -0.408248291 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -0.408248291 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -0.408248291 + -0.25 x = -0.408248291 + -0.25 Combine like terms: -0.408248291 + -0.25 = -0.658248291 x = -0.658248291 Simplifying x = -0.658248291Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.158248291, -0.658248291}
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