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Simplifying 5y(3y + -8) + 32 = 0 Reorder the terms: 5y(-8 + 3y) + 32 = 0 (-8 * 5y + 3y * 5y) + 32 = 0 (-40y + 15y2) + 32 = 0 Reorder the terms: 32 + -40y + 15y2 = 0 Solving 32 + -40y + 15y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 2.133333333 + -2.666666667y + y2 = 0 Move the constant term to the right: Add '-2.133333333' to each side of the equation. 2.133333333 + -2.666666667y + -2.133333333 + y2 = 0 + -2.133333333 Reorder the terms: 2.133333333 + -2.133333333 + -2.666666667y + y2 = 0 + -2.133333333 Combine like terms: 2.133333333 + -2.133333333 = 0.000000000 0.000000000 + -2.666666667y + y2 = 0 + -2.133333333 -2.666666667y + y2 = 0 + -2.133333333 Combine like terms: 0 + -2.133333333 = -2.133333333 -2.666666667y + y2 = -2.133333333 The y term is -2.666666667y. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667y + 1.777777780 + y2 = -2.133333333 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667y + y2 = -2.133333333 + 1.777777780 Combine like terms: -2.133333333 + 1.777777780 = -0.355555553 1.777777780 + -2.666666667y + y2 = -0.355555553 Factor a perfect square on the left side: (y + -1.333333334)(y + -1.333333334) = -0.355555553 Can't calculate square root of the right side. The solution to this equation could not be determined.
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