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Simplifying 8x + -40 = 6x2 + -5x + 100 Reorder the terms: -40 + 8x = 6x2 + -5x + 100 Reorder the terms: -40 + 8x = 100 + -5x + 6x2 Solving -40 + 8x = 100 + -5x + 6x2 Solving for variable 'x'. Reorder the terms: -40 + -100 + 8x + 5x + -6x2 = 100 + -5x + 6x2 + -100 + 5x + -6x2 Combine like terms: -40 + -100 = -140 -140 + 8x + 5x + -6x2 = 100 + -5x + 6x2 + -100 + 5x + -6x2 Combine like terms: 8x + 5x = 13x -140 + 13x + -6x2 = 100 + -5x + 6x2 + -100 + 5x + -6x2 Reorder the terms: -140 + 13x + -6x2 = 100 + -100 + -5x + 5x + 6x2 + -6x2 Combine like terms: 100 + -100 = 0 -140 + 13x + -6x2 = 0 + -5x + 5x + 6x2 + -6x2 -140 + 13x + -6x2 = -5x + 5x + 6x2 + -6x2 Combine like terms: -5x + 5x = 0 -140 + 13x + -6x2 = 0 + 6x2 + -6x2 -140 + 13x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -140 + 13x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. 23.33333333 + -2.166666667x + x2 = 0 Move the constant term to the right: Add '-23.33333333' to each side of the equation. 23.33333333 + -2.166666667x + -23.33333333 + x2 = 0 + -23.33333333 Reorder the terms: 23.33333333 + -23.33333333 + -2.166666667x + x2 = 0 + -23.33333333 Combine like terms: 23.33333333 + -23.33333333 = 0.00000000 0.00000000 + -2.166666667x + x2 = 0 + -23.33333333 -2.166666667x + x2 = 0 + -23.33333333 Combine like terms: 0 + -23.33333333 = -23.33333333 -2.166666667x + x2 = -23.33333333 The x term is -2.166666667x. Take half its coefficient (-1.083333334). Square it (1.173611113) and add it to both sides. Add '1.173611113' to each side of the equation. -2.166666667x + 1.173611113 + x2 = -23.33333333 + 1.173611113 Reorder the terms: 1.173611113 + -2.166666667x + x2 = -23.33333333 + 1.173611113 Combine like terms: -23.33333333 + 1.173611113 = -22.159722217 1.173611113 + -2.166666667x + x2 = -22.159722217 Factor a perfect square on the left side: (x + -1.083333334)(x + -1.083333334) = -22.159722217 Can't calculate square root of the right side. The solution to this equation could not be determined.
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