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Simplifying -4y2 + 1 = -6y Reorder the terms: 1 + -4y2 = -6y Solving 1 + -4y2 = -6y Solving for variable 'y'. Reorder the terms: 1 + 6y + -4y2 = -6y + 6y Combine like terms: -6y + 6y = 0 1 + 6y + -4y2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.25 + -1.5y + y2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -1.5y + 0.25 + y2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -1.5y + y2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -1.5y + y2 = 0 + 0.25 -1.5y + y2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -1.5y + y2 = 0.25 The y term is -1.5y. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5y + 0.5625 + y2 = 0.25 + 0.5625 Reorder the terms: 0.5625 + -1.5y + y2 = 0.25 + 0.5625 Combine like terms: 0.25 + 0.5625 = 0.8125 0.5625 + -1.5y + y2 = 0.8125 Factor a perfect square on the left side: (y + -0.75)(y + -0.75) = 0.8125 Calculate the square root of the right side: 0.901387819 Break this problem into two subproblems by setting (y + -0.75) equal to 0.901387819 and -0.901387819.Subproblem 1
y + -0.75 = 0.901387819 Simplifying y + -0.75 = 0.901387819 Reorder the terms: -0.75 + y = 0.901387819 Solving -0.75 + y = 0.901387819 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + y = 0.901387819 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + y = 0.901387819 + 0.75 y = 0.901387819 + 0.75 Combine like terms: 0.901387819 + 0.75 = 1.651387819 y = 1.651387819 Simplifying y = 1.651387819Subproblem 2
y + -0.75 = -0.901387819 Simplifying y + -0.75 = -0.901387819 Reorder the terms: -0.75 + y = -0.901387819 Solving -0.75 + y = -0.901387819 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + y = -0.901387819 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + y = -0.901387819 + 0.75 y = -0.901387819 + 0.75 Combine like terms: -0.901387819 + 0.75 = -0.151387819 y = -0.151387819 Simplifying y = -0.151387819Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.651387819, -0.151387819}
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