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Simplifying -5y2 + 57y + 40 = 0 Reorder the terms: 40 + 57y + -5y2 = 0 Solving 40 + 57y + -5y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -8 + -11.4y + y2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -11.4y + 8 + y2 = 0 + 8 Reorder the terms: -8 + 8 + -11.4y + y2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -11.4y + y2 = 0 + 8 -11.4y + y2 = 0 + 8 Combine like terms: 0 + 8 = 8 -11.4y + y2 = 8 The y term is -11.4y. Take half its coefficient (-5.7). Square it (32.49) and add it to both sides. Add '32.49' to each side of the equation. -11.4y + 32.49 + y2 = 8 + 32.49 Reorder the terms: 32.49 + -11.4y + y2 = 8 + 32.49 Combine like terms: 8 + 32.49 = 40.49 32.49 + -11.4y + y2 = 40.49 Factor a perfect square on the left side: (y + -5.7)(y + -5.7) = 40.49 Calculate the square root of the right side: 6.363175308 Break this problem into two subproblems by setting (y + -5.7) equal to 6.363175308 and -6.363175308.Subproblem 1
y + -5.7 = 6.363175308 Simplifying y + -5.7 = 6.363175308 Reorder the terms: -5.7 + y = 6.363175308 Solving -5.7 + y = 6.363175308 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.7' to each side of the equation. -5.7 + 5.7 + y = 6.363175308 + 5.7 Combine like terms: -5.7 + 5.7 = 0.0 0.0 + y = 6.363175308 + 5.7 y = 6.363175308 + 5.7 Combine like terms: 6.363175308 + 5.7 = 12.063175308 y = 12.063175308 Simplifying y = 12.063175308Subproblem 2
y + -5.7 = -6.363175308 Simplifying y + -5.7 = -6.363175308 Reorder the terms: -5.7 + y = -6.363175308 Solving -5.7 + y = -6.363175308 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.7' to each side of the equation. -5.7 + 5.7 + y = -6.363175308 + 5.7 Combine like terms: -5.7 + 5.7 = 0.0 0.0 + y = -6.363175308 + 5.7 y = -6.363175308 + 5.7 Combine like terms: -6.363175308 + 5.7 = -0.663175308 y = -0.663175308 Simplifying y = -0.663175308Solution
The solution to the problem is based on the solutions from the subproblems. y = {12.063175308, -0.663175308}
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