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Simplifying 0.8x(x + -5) = 1 + -0.3(10 + -2x) + -0.5 Reorder the terms: 0.8x(-5 + x) = 1 + -0.3(10 + -2x) + -0.5 (-5 * 0.8x + x * 0.8x) = 1 + -0.3(10 + -2x) + -0.5 (-4x + 0.8x2) = 1 + -0.3(10 + -2x) + -0.5 -4x + 0.8x2 = 1 + (10 * -0.3 + -2x * -0.3) + -0.5 -4x + 0.8x2 = 1 + (-3 + 0.6x) + -0.5 Reorder the terms: -4x + 0.8x2 = 1 + -3 + -0.5 + 0.6x Combine like terms: 1 + -3 = -2 -4x + 0.8x2 = -2 + -0.5 + 0.6x Combine like terms: -2 + -0.5 = -2.5 -4x + 0.8x2 = -2.5 + 0.6x Solving -4x + 0.8x2 = -2.5 + 0.6x Solving for variable 'x'. Reorder the terms: 2.5 + -4x + -0.6x + 0.8x2 = -2.5 + 0.6x + 2.5 + -0.6x Combine like terms: -4x + -0.6x = -4.6x 2.5 + -4.6x + 0.8x2 = -2.5 + 0.6x + 2.5 + -0.6x Reorder the terms: 2.5 + -4.6x + 0.8x2 = -2.5 + 2.5 + 0.6x + -0.6x Combine like terms: -2.5 + 2.5 = 0.0 2.5 + -4.6x + 0.8x2 = 0.0 + 0.6x + -0.6x 2.5 + -4.6x + 0.8x2 = 0.6x + -0.6x Combine like terms: 0.6x + -0.6x = 0.0 2.5 + -4.6x + 0.8x2 = 0.0 Begin completing the square. Divide all terms by 0.8 the coefficient of the squared term: Divide each side by '0.8'. 3.125 + -5.75x + x2 = 0 Move the constant term to the right: Add '-3.125' to each side of the equation. 3.125 + -5.75x + -3.125 + x2 = 0 + -3.125 Reorder the terms: 3.125 + -3.125 + -5.75x + x2 = 0 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + -5.75x + x2 = 0 + -3.125 -5.75x + x2 = 0 + -3.125 Combine like terms: 0 + -3.125 = -3.125 -5.75x + x2 = -3.125 The x term is -5.75x. Take half its coefficient (-2.875). Square it (8.265625) and add it to both sides. Add '8.265625' to each side of the equation. -5.75x + 8.265625 + x2 = -3.125 + 8.265625 Reorder the terms: 8.265625 + -5.75x + x2 = -3.125 + 8.265625 Combine like terms: -3.125 + 8.265625 = 5.140625 8.265625 + -5.75x + x2 = 5.140625 Factor a perfect square on the left side: (x + -2.875)(x + -2.875) = 5.140625 Calculate the square root of the right side: 2.267294643 Break this problem into two subproblems by setting (x + -2.875) equal to 2.267294643 and -2.267294643.Subproblem 1
x + -2.875 = 2.267294643 Simplifying x + -2.875 = 2.267294643 Reorder the terms: -2.875 + x = 2.267294643 Solving -2.875 + x = 2.267294643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + x = 2.267294643 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = 2.267294643 + 2.875 x = 2.267294643 + 2.875 Combine like terms: 2.267294643 + 2.875 = 5.142294643 x = 5.142294643 Simplifying x = 5.142294643Subproblem 2
x + -2.875 = -2.267294643 Simplifying x + -2.875 = -2.267294643 Reorder the terms: -2.875 + x = -2.267294643 Solving -2.875 + x = -2.267294643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + x = -2.267294643 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = -2.267294643 + 2.875 x = -2.267294643 + 2.875 Combine like terms: -2.267294643 + 2.875 = 0.607705357 x = 0.607705357 Simplifying x = 0.607705357Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.142294643, 0.607705357}
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