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Simplifying 4y2 + 5y = 15 Reorder the terms: 5y + 4y2 = 15 Solving 5y + 4y2 = 15 Solving for variable 'y'. Reorder the terms: -15 + 5y + 4y2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 5y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + 1.25y + y2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + 1.25y + 3.75 + y2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + 1.25y + y2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + 1.25y + y2 = 0 + 3.75 1.25y + y2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 1.25y + y2 = 3.75 The y term is 1.25y. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25y + 0.390625 + y2 = 3.75 + 0.390625 Reorder the terms: 0.390625 + 1.25y + y2 = 3.75 + 0.390625 Combine like terms: 3.75 + 0.390625 = 4.140625 0.390625 + 1.25y + y2 = 4.140625 Factor a perfect square on the left side: (y + 0.625)(y + 0.625) = 4.140625 Calculate the square root of the right side: 2.034852575 Break this problem into two subproblems by setting (y + 0.625) equal to 2.034852575 and -2.034852575.Subproblem 1
y + 0.625 = 2.034852575 Simplifying y + 0.625 = 2.034852575 Reorder the terms: 0.625 + y = 2.034852575 Solving 0.625 + y = 2.034852575 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + y = 2.034852575 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + y = 2.034852575 + -0.625 y = 2.034852575 + -0.625 Combine like terms: 2.034852575 + -0.625 = 1.409852575 y = 1.409852575 Simplifying y = 1.409852575Subproblem 2
y + 0.625 = -2.034852575 Simplifying y + 0.625 = -2.034852575 Reorder the terms: 0.625 + y = -2.034852575 Solving 0.625 + y = -2.034852575 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + y = -2.034852575 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + y = -2.034852575 + -0.625 y = -2.034852575 + -0.625 Combine like terms: -2.034852575 + -0.625 = -2.659852575 y = -2.659852575 Simplifying y = -2.659852575Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.409852575, -2.659852575}
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