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Simplifying 4y2 + -8y + 4 + 3y + -3 = 8 Reorder the terms: 4 + -3 + -8y + 3y + 4y2 = 8 Combine like terms: 4 + -3 = 1 1 + -8y + 3y + 4y2 = 8 Combine like terms: -8y + 3y = -5y 1 + -5y + 4y2 = 8 Solving 1 + -5y + 4y2 = 8 Solving for variable 'y'. Reorder the terms: 1 + -8 + -5y + 4y2 = 8 + -8 Combine like terms: 1 + -8 = -7 -7 + -5y + 4y2 = 8 + -8 Combine like terms: 8 + -8 = 0 -7 + -5y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.75 + -1.25y + y2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -1.25y + 1.75 + y2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -1.25y + y2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -1.25y + y2 = 0 + 1.75 -1.25y + y2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -1.25y + y2 = 1.75 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 = 1.75 + 0.390625 Reorder the terms: 0.390625 + -1.25y + y2 = 1.75 + 0.390625 Combine like terms: 1.75 + 0.390625 = 2.140625 0.390625 + -1.25y + y2 = 2.140625 Factor a perfect square on the left side: (y + -0.625)(y + -0.625) = 2.140625 Calculate the square root of the right side: 1.463087489 Break this problem into two subproblems by setting (y + -0.625) equal to 1.463087489 and -1.463087489.Subproblem 1
y + -0.625 = 1.463087489 Simplifying y + -0.625 = 1.463087489 Reorder the terms: -0.625 + y = 1.463087489 Solving -0.625 + y = 1.463087489 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 = 1.463087489 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + y = 1.463087489 + 0.625 y = 1.463087489 + 0.625 Combine like terms: 1.463087489 + 0.625 = 2.088087489 y = 2.088087489 Simplifying y = 2.088087489Subproblem 2
y + -0.625 = -1.463087489 Simplifying y + -0.625 = -1.463087489 Reorder the terms: -0.625 + y = -1.463087489 Solving -0.625 + y = -1.463087489 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 = -1.463087489 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + y = -1.463087489 + 0.625 y = -1.463087489 + 0.625 Combine like terms: -1.463087489 + 0.625 = -0.838087489 y = -0.838087489 Simplifying y = -0.838087489Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.088087489, -0.838087489}
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