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Simplifying -4y2 + 4y = -9 Reorder the terms: 4y + -4y2 = -9 Solving 4y + -4y2 = -9 Solving for variable 'y'. Reorder the terms: 9 + 4y + -4y2 = -9 + 9 Combine like terms: -9 + 9 = 0 9 + 4y + -4y2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -2.25 + -1y + y2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -1y + 2.25 + y2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -1y + y2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -1y + y2 = 0 + 2.25 -1y + y2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -1y + y2 = 2.25 The y term is -1y. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1y + 0.25 + y2 = 2.25 + 0.25 Reorder the terms: 0.25 + -1y + y2 = 2.25 + 0.25 Combine like terms: 2.25 + 0.25 = 2.5 0.25 + -1y + y2 = 2.5 Factor a perfect square on the left side: (y + -0.5)(y + -0.5) = 2.5 Calculate the square root of the right side: 1.58113883 Break this problem into two subproblems by setting (y + -0.5) equal to 1.58113883 and -1.58113883.Subproblem 1
y + -0.5 = 1.58113883 Simplifying y + -0.5 = 1.58113883 Reorder the terms: -0.5 + y = 1.58113883 Solving -0.5 + y = 1.58113883 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = 1.58113883 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = 1.58113883 + 0.5 y = 1.58113883 + 0.5 Combine like terms: 1.58113883 + 0.5 = 2.08113883 y = 2.08113883 Simplifying y = 2.08113883Subproblem 2
y + -0.5 = -1.58113883 Simplifying y + -0.5 = -1.58113883 Reorder the terms: -0.5 + y = -1.58113883 Solving -0.5 + y = -1.58113883 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = -1.58113883 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = -1.58113883 + 0.5 y = -1.58113883 + 0.5 Combine like terms: -1.58113883 + 0.5 = -1.08113883 y = -1.08113883 Simplifying y = -1.08113883Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.08113883, -1.08113883}
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