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Simplifying -2y2 + 19y + 15 = 0 Reorder the terms: 15 + 19y + -2y2 = 0 Solving 15 + 19y + -2y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -7.5 + -9.5y + y2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -9.5y + 7.5 + y2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -9.5y + y2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -9.5y + y2 = 0 + 7.5 -9.5y + y2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -9.5y + y2 = 7.5 The y term is -9.5y. Take half its coefficient (-4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. -9.5y + 22.5625 + y2 = 7.5 + 22.5625 Reorder the terms: 22.5625 + -9.5y + y2 = 7.5 + 22.5625 Combine like terms: 7.5 + 22.5625 = 30.0625 22.5625 + -9.5y + y2 = 30.0625 Factor a perfect square on the left side: (y + -4.75)(y + -4.75) = 30.0625 Calculate the square root of the right side: 5.48292805 Break this problem into two subproblems by setting (y + -4.75) equal to 5.48292805 and -5.48292805.Subproblem 1
y + -4.75 = 5.48292805 Simplifying y + -4.75 = 5.48292805 Reorder the terms: -4.75 + y = 5.48292805 Solving -4.75 + y = 5.48292805 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + y = 5.48292805 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + y = 5.48292805 + 4.75 y = 5.48292805 + 4.75 Combine like terms: 5.48292805 + 4.75 = 10.23292805 y = 10.23292805 Simplifying y = 10.23292805Subproblem 2
y + -4.75 = -5.48292805 Simplifying y + -4.75 = -5.48292805 Reorder the terms: -4.75 + y = -5.48292805 Solving -4.75 + y = -5.48292805 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + y = -5.48292805 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + y = -5.48292805 + 4.75 y = -5.48292805 + 4.75 Combine like terms: -5.48292805 + 4.75 = -0.73292805 y = -0.73292805 Simplifying y = -0.73292805Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.23292805, -0.73292805}
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