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Simplifying 8x(x + -5) = 5x + 12 Reorder the terms: 8x(-5 + x) = 5x + 12 (-5 * 8x + x * 8x) = 5x + 12 (-40x + 8x2) = 5x + 12 Reorder the terms: -40x + 8x2 = 12 + 5x Solving -40x + 8x2 = 12 + 5x Solving for variable 'x'. Reorder the terms: -12 + -40x + -5x + 8x2 = 12 + 5x + -12 + -5x Combine like terms: -40x + -5x = -45x -12 + -45x + 8x2 = 12 + 5x + -12 + -5x Reorder the terms: -12 + -45x + 8x2 = 12 + -12 + 5x + -5x Combine like terms: 12 + -12 = 0 -12 + -45x + 8x2 = 0 + 5x + -5x -12 + -45x + 8x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -12 + -45x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.5 + -5.625x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -5.625x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -5.625x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -5.625x + x2 = 0 + 1.5 -5.625x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -5.625x + x2 = 1.5 The x term is -5.625x. Take half its coefficient (-2.8125). Square it (7.91015625) and add it to both sides. Add '7.91015625' to each side of the equation. -5.625x + 7.91015625 + x2 = 1.5 + 7.91015625 Reorder the terms: 7.91015625 + -5.625x + x2 = 1.5 + 7.91015625 Combine like terms: 1.5 + 7.91015625 = 9.41015625 7.91015625 + -5.625x + x2 = 9.41015625 Factor a perfect square on the left side: (x + -2.8125)(x + -2.8125) = 9.41015625 Calculate the square root of the right side: 3.067597798 Break this problem into two subproblems by setting (x + -2.8125) equal to 3.067597798 and -3.067597798.Subproblem 1
x + -2.8125 = 3.067597798 Simplifying x + -2.8125 = 3.067597798 Reorder the terms: -2.8125 + x = 3.067597798 Solving -2.8125 + x = 3.067597798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8125' to each side of the equation. -2.8125 + 2.8125 + x = 3.067597798 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + x = 3.067597798 + 2.8125 x = 3.067597798 + 2.8125 Combine like terms: 3.067597798 + 2.8125 = 5.880097798 x = 5.880097798 Simplifying x = 5.880097798Subproblem 2
x + -2.8125 = -3.067597798 Simplifying x + -2.8125 = -3.067597798 Reorder the terms: -2.8125 + x = -3.067597798 Solving -2.8125 + x = -3.067597798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8125' to each side of the equation. -2.8125 + 2.8125 + x = -3.067597798 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + x = -3.067597798 + 2.8125 x = -3.067597798 + 2.8125 Combine like terms: -3.067597798 + 2.8125 = -0.255097798 x = -0.255097798 Simplifying x = -0.255097798Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.880097798, -0.255097798}
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