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Simplifying 2y2 + 3 = -8y Reorder the terms: 3 + 2y2 = -8y Solving 3 + 2y2 = -8y Solving for variable 'y'. Reorder the terms: 3 + 8y + 2y2 = -8y + 8y Combine like terms: -8y + 8y = 0 3 + 8y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + 4y + y2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 4y + -1.5 + y2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 4y + y2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 4y + y2 = 0 + -1.5 4y + y2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 4y + y2 = -1.5 The y term is 4y. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4y + 4 + y2 = -1.5 + 4 Reorder the terms: 4 + 4y + y2 = -1.5 + 4 Combine like terms: -1.5 + 4 = 2.5 4 + 4y + y2 = 2.5 Factor a perfect square on the left side: (y + 2)(y + 2) = 2.5 Calculate the square root of the right side: 1.58113883 Break this problem into two subproblems by setting (y + 2) equal to 1.58113883 and -1.58113883.Subproblem 1
y + 2 = 1.58113883 Simplifying y + 2 = 1.58113883 Reorder the terms: 2 + y = 1.58113883 Solving 2 + y = 1.58113883 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = 1.58113883 + -2 Combine like terms: 2 + -2 = 0 0 + y = 1.58113883 + -2 y = 1.58113883 + -2 Combine like terms: 1.58113883 + -2 = -0.41886117 y = -0.41886117 Simplifying y = -0.41886117Subproblem 2
y + 2 = -1.58113883 Simplifying y + 2 = -1.58113883 Reorder the terms: 2 + y = -1.58113883 Solving 2 + y = -1.58113883 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = -1.58113883 + -2 Combine like terms: 2 + -2 = 0 0 + y = -1.58113883 + -2 y = -1.58113883 + -2 Combine like terms: -1.58113883 + -2 = -3.58113883 y = -3.58113883 Simplifying y = -3.58113883Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.41886117, -3.58113883}
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