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Simplifying -5y2 + 8y = -12 Reorder the terms: 8y + -5y2 = -12 Solving 8y + -5y2 = -12 Solving for variable 'y'. Reorder the terms: 12 + 8y + -5y2 = -12 + 12 Combine like terms: -12 + 12 = 0 12 + 8y + -5y2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -2.4 + -1.6y + y2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + -1.6y + 2.4 + y2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + -1.6y + y2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + -1.6y + y2 = 0 + 2.4 -1.6y + y2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 -1.6y + y2 = 2.4 The y term is -1.6y. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6y + 0.64 + y2 = 2.4 + 0.64 Reorder the terms: 0.64 + -1.6y + y2 = 2.4 + 0.64 Combine like terms: 2.4 + 0.64 = 3.04 0.64 + -1.6y + y2 = 3.04 Factor a perfect square on the left side: (y + -0.8)(y + -0.8) = 3.04 Calculate the square root of the right side: 1.743559577 Break this problem into two subproblems by setting (y + -0.8) equal to 1.743559577 and -1.743559577.Subproblem 1
y + -0.8 = 1.743559577 Simplifying y + -0.8 = 1.743559577 Reorder the terms: -0.8 + y = 1.743559577 Solving -0.8 + y = 1.743559577 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + y = 1.743559577 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + y = 1.743559577 + 0.8 y = 1.743559577 + 0.8 Combine like terms: 1.743559577 + 0.8 = 2.543559577 y = 2.543559577 Simplifying y = 2.543559577Subproblem 2
y + -0.8 = -1.743559577 Simplifying y + -0.8 = -1.743559577 Reorder the terms: -0.8 + y = -1.743559577 Solving -0.8 + y = -1.743559577 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + y = -1.743559577 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + y = -1.743559577 + 0.8 y = -1.743559577 + 0.8 Combine like terms: -1.743559577 + 0.8 = -0.943559577 y = -0.943559577 Simplifying y = -0.943559577Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.543559577, -0.943559577}
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