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Simplifying -5(8x + -6) + -1x(x + 6) = 0 Reorder the terms: -5(-6 + 8x) + -1x(x + 6) = 0 (-6 * -5 + 8x * -5) + -1x(x + 6) = 0 (30 + -40x) + -1x(x + 6) = 0 Reorder the terms: 30 + -40x + -1x(6 + x) = 0 30 + -40x + (6 * -1x + x * -1x) = 0 30 + -40x + (-6x + -1x2) = 0 Combine like terms: -40x + -6x = -46x 30 + -46x + -1x2 = 0 Solving 30 + -46x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -30 + 46x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + 46x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 46x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 46x + x2 = 0 + 30 46x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 46x + x2 = 30 The x term is 46x. Take half its coefficient (23). Square it (529) and add it to both sides. Add '529' to each side of the equation. 46x + 529 + x2 = 30 + 529 Reorder the terms: 529 + 46x + x2 = 30 + 529 Combine like terms: 30 + 529 = 559 529 + 46x + x2 = 559 Factor a perfect square on the left side: (x + 23)(x + 23) = 559 Calculate the square root of the right side: 23.643180835 Break this problem into two subproblems by setting (x + 23) equal to 23.643180835 and -23.643180835.Subproblem 1
x + 23 = 23.643180835 Simplifying x + 23 = 23.643180835 Reorder the terms: 23 + x = 23.643180835 Solving 23 + x = 23.643180835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + x = 23.643180835 + -23 Combine like terms: 23 + -23 = 0 0 + x = 23.643180835 + -23 x = 23.643180835 + -23 Combine like terms: 23.643180835 + -23 = 0.643180835 x = 0.643180835 Simplifying x = 0.643180835Subproblem 2
x + 23 = -23.643180835 Simplifying x + 23 = -23.643180835 Reorder the terms: 23 + x = -23.643180835 Solving 23 + x = -23.643180835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + x = -23.643180835 + -23 Combine like terms: 23 + -23 = 0 0 + x = -23.643180835 + -23 x = -23.643180835 + -23 Combine like terms: -23.643180835 + -23 = -46.643180835 x = -46.643180835 Simplifying x = -46.643180835Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.643180835, -46.643180835}
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