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Simplifying 0.20(y + -2) * 0.12y = 0.16y + -0.03(40) Reorder the terms: 0.20(-2 + y) * 0.12y = 0.16y + -0.03(40) Reorder the terms for easier multiplication: 0.20 * 0.12y(-2 + y) = 0.16y + -0.03(40) Multiply 0.20 * 0.12 0.024y(-2 + y) = 0.16y + -0.03(40) (-2 * 0.024y + y * 0.024y) = 0.16y + -0.03(40) (-0.048y + 0.024y2) = 0.16y + -0.03(40) Multiply -0.03 * 40 -0.048y + 0.024y2 = 0.16y + -1.2 Reorder the terms: -0.048y + 0.024y2 = -1.2 + 0.16y Solving -0.048y + 0.024y2 = -1.2 + 0.16y Solving for variable 'y'. Reorder the terms: 1.2 + -0.048y + -0.16y + 0.024y2 = -1.2 + 0.16y + 1.2 + -0.16y Combine like terms: -0.048y + -0.16y = -0.208y 1.2 + -0.208y + 0.024y2 = -1.2 + 0.16y + 1.2 + -0.16y Reorder the terms: 1.2 + -0.208y + 0.024y2 = -1.2 + 1.2 + 0.16y + -0.16y Combine like terms: -1.2 + 1.2 = 0.0 1.2 + -0.208y + 0.024y2 = 0.0 + 0.16y + -0.16y 1.2 + -0.208y + 0.024y2 = 0.16y + -0.16y Combine like terms: 0.16y + -0.16y = 0.00 1.2 + -0.208y + 0.024y2 = 0.00 Begin completing the square. Divide all terms by 0.024 the coefficient of the squared term: Divide each side by '0.024'. 50 + -8.666666667y + y2 = 0 Move the constant term to the right: Add '-50' to each side of the equation. 50 + -8.666666667y + -50 + y2 = 0 + -50 Reorder the terms: 50 + -50 + -8.666666667y + y2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -8.666666667y + y2 = 0 + -50 -8.666666667y + y2 = 0 + -50 Combine like terms: 0 + -50 = -50 -8.666666667y + y2 = -50 The y term is -8.666666667y. Take half its coefficient (-4.333333334). Square it (18.77777778) and add it to both sides. Add '18.77777778' to each side of the equation. -8.666666667y + 18.77777778 + y2 = -50 + 18.77777778 Reorder the terms: 18.77777778 + -8.666666667y + y2 = -50 + 18.77777778 Combine like terms: -50 + 18.77777778 = -31.22222222 18.77777778 + -8.666666667y + y2 = -31.22222222 Factor a perfect square on the left side: (y + -4.333333334)(y + -4.333333334) = -31.22222222 Can't calculate square root of the right side. The solution to this equation could not be determined.
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