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Simplifying 2(x + 8) * 3x = 5 Reorder the terms: 2(8 + x) * 3x = 5 Reorder the terms for easier multiplication: 2 * 3x(8 + x) = 5 Multiply 2 * 3 6x(8 + x) = 5 (8 * 6x + x * 6x) = 5 (48x + 6x2) = 5 Solving 48x + 6x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 48x + 6x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 48x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.8333333333 + 8x + x2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + 8x + 0.8333333333 + x2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + 8x + x2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + 8x + x2 = 0 + 0.8333333333 8x + x2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 8x + x2 = 0.8333333333 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 0.8333333333 + 16 Reorder the terms: 16 + 8x + x2 = 0.8333333333 + 16 Combine like terms: 0.8333333333 + 16 = 16.8333333333 16 + 8x + x2 = 16.8333333333 Factor a perfect square on the left side: (x + 4)(x + 4) = 16.8333333333 Calculate the square root of the right side: 4.102844542 Break this problem into two subproblems by setting (x + 4) equal to 4.102844542 and -4.102844542.Subproblem 1
x + 4 = 4.102844542 Simplifying x + 4 = 4.102844542 Reorder the terms: 4 + x = 4.102844542 Solving 4 + x = 4.102844542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 4.102844542 + -4 Combine like terms: 4 + -4 = 0 0 + x = 4.102844542 + -4 x = 4.102844542 + -4 Combine like terms: 4.102844542 + -4 = 0.102844542 x = 0.102844542 Simplifying x = 0.102844542Subproblem 2
x + 4 = -4.102844542 Simplifying x + 4 = -4.102844542 Reorder the terms: 4 + x = -4.102844542 Solving 4 + x = -4.102844542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -4.102844542 + -4 Combine like terms: 4 + -4 = 0 0 + x = -4.102844542 + -4 x = -4.102844542 + -4 Combine like terms: -4.102844542 + -4 = -8.102844542 x = -8.102844542 Simplifying x = -8.102844542Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.102844542, -8.102844542}
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