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Simplifying 4y(5y + -9) + -24y + 70 = 4(1 + -21y) Reorder the terms: 4y(-9 + 5y) + -24y + 70 = 4(1 + -21y) (-9 * 4y + 5y * 4y) + -24y + 70 = 4(1 + -21y) (-36y + 20y2) + -24y + 70 = 4(1 + -21y) Reorder the terms: 70 + -36y + -24y + 20y2 = 4(1 + -21y) Combine like terms: -36y + -24y = -60y 70 + -60y + 20y2 = 4(1 + -21y) 70 + -60y + 20y2 = (1 * 4 + -21y * 4) 70 + -60y + 20y2 = (4 + -84y) Solving 70 + -60y + 20y2 = 4 + -84y Solving for variable 'y'. Reorder the terms: 70 + -4 + -60y + 84y + 20y2 = 4 + -84y + -4 + 84y Combine like terms: 70 + -4 = 66 66 + -60y + 84y + 20y2 = 4 + -84y + -4 + 84y Combine like terms: -60y + 84y = 24y 66 + 24y + 20y2 = 4 + -84y + -4 + 84y Reorder the terms: 66 + 24y + 20y2 = 4 + -4 + -84y + 84y Combine like terms: 4 + -4 = 0 66 + 24y + 20y2 = 0 + -84y + 84y 66 + 24y + 20y2 = -84y + 84y Combine like terms: -84y + 84y = 0 66 + 24y + 20y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(33 + 12y + 10y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(33 + 12y + 10y2)' equal to zero and attempt to solve: Simplifying 33 + 12y + 10y2 = 0 Solving 33 + 12y + 10y2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 3.3 + 1.2y + y2 = 0.0 Move the constant term to the right: Add '-3.3' to each side of the equation. 3.3 + 1.2y + -3.3 + y2 = 0.0 + -3.3 Reorder the terms: 3.3 + -3.3 + 1.2y + y2 = 0.0 + -3.3 Combine like terms: 3.3 + -3.3 = 0.0 0.0 + 1.2y + y2 = 0.0 + -3.3 1.2y + y2 = 0.0 + -3.3 Combine like terms: 0.0 + -3.3 = -3.3 1.2y + y2 = -3.3 The y term is 1.2y. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2y + 0.36 + y2 = -3.3 + 0.36 Reorder the terms: 0.36 + 1.2y + y2 = -3.3 + 0.36 Combine like terms: -3.3 + 0.36 = -2.94 0.36 + 1.2y + y2 = -2.94 Factor a perfect square on the left side: (y + 0.6)(y + 0.6) = -2.94 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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