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Simplifying 8x(x + -5) = 4x + -10 + 3x + -30 Reorder the terms: 8x(-5 + x) = 4x + -10 + 3x + -30 (-5 * 8x + x * 8x) = 4x + -10 + 3x + -30 (-40x + 8x2) = 4x + -10 + 3x + -30 Reorder the terms: -40x + 8x2 = -10 + -30 + 4x + 3x Combine like terms: -10 + -30 = -40 -40x + 8x2 = -40 + 4x + 3x Combine like terms: 4x + 3x = 7x -40x + 8x2 = -40 + 7x Solving -40x + 8x2 = -40 + 7x Solving for variable 'x'. Reorder the terms: 40 + -40x + -7x + 8x2 = -40 + 7x + 40 + -7x Combine like terms: -40x + -7x = -47x 40 + -47x + 8x2 = -40 + 7x + 40 + -7x Reorder the terms: 40 + -47x + 8x2 = -40 + 40 + 7x + -7x Combine like terms: -40 + 40 = 0 40 + -47x + 8x2 = 0 + 7x + -7x 40 + -47x + 8x2 = 7x + -7x Combine like terms: 7x + -7x = 0 40 + -47x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 5 + -5.875x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -5.875x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -5.875x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -5.875x + x2 = 0 + -5 -5.875x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -5.875x + x2 = -5 The x term is -5.875x. Take half its coefficient (-2.9375). Square it (8.62890625) and add it to both sides. Add '8.62890625' to each side of the equation. -5.875x + 8.62890625 + x2 = -5 + 8.62890625 Reorder the terms: 8.62890625 + -5.875x + x2 = -5 + 8.62890625 Combine like terms: -5 + 8.62890625 = 3.62890625 8.62890625 + -5.875x + x2 = 3.62890625 Factor a perfect square on the left side: (x + -2.9375)(x + -2.9375) = 3.62890625 Calculate the square root of the right side: 1.904968832 Break this problem into two subproblems by setting (x + -2.9375) equal to 1.904968832 and -1.904968832.Subproblem 1
x + -2.9375 = 1.904968832 Simplifying x + -2.9375 = 1.904968832 Reorder the terms: -2.9375 + x = 1.904968832 Solving -2.9375 + x = 1.904968832 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.9375' to each side of the equation. -2.9375 + 2.9375 + x = 1.904968832 + 2.9375 Combine like terms: -2.9375 + 2.9375 = 0.0000 0.0000 + x = 1.904968832 + 2.9375 x = 1.904968832 + 2.9375 Combine like terms: 1.904968832 + 2.9375 = 4.842468832 x = 4.842468832 Simplifying x = 4.842468832Subproblem 2
x + -2.9375 = -1.904968832 Simplifying x + -2.9375 = -1.904968832 Reorder the terms: -2.9375 + x = -1.904968832 Solving -2.9375 + x = -1.904968832 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.9375' to each side of the equation. -2.9375 + 2.9375 + x = -1.904968832 + 2.9375 Combine like terms: -2.9375 + 2.9375 = 0.0000 0.0000 + x = -1.904968832 + 2.9375 x = -1.904968832 + 2.9375 Combine like terms: -1.904968832 + 2.9375 = 1.032531168 x = 1.032531168 Simplifying x = 1.032531168Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.842468832, 1.032531168}
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