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Simplifying 4y + 33 = 4y2 Reorder the terms: 33 + 4y = 4y2 Solving 33 + 4y = 4y2 Solving for variable 'y'. Combine like terms: 4y2 + -4y2 = 0 33 + 4y + -4y2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -8.25 + -1y + y2 = 0 Move the constant term to the right: Add '8.25' to each side of the equation. -8.25 + -1y + 8.25 + y2 = 0 + 8.25 Reorder the terms: -8.25 + 8.25 + -1y + y2 = 0 + 8.25 Combine like terms: -8.25 + 8.25 = 0.00 0.00 + -1y + y2 = 0 + 8.25 -1y + y2 = 0 + 8.25 Combine like terms: 0 + 8.25 = 8.25 -1y + y2 = 8.25 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 = 8.25 + 0.25 Reorder the terms: 0.25 + -1y + y2 = 8.25 + 0.25 Combine like terms: 8.25 + 0.25 = 8.5 0.25 + -1y + y2 = 8.5 Factor a perfect square on the left side: (y + -0.5)(y + -0.5) = 8.5 Calculate the square root of the right side: 2.915475947 Break this problem into two subproblems by setting (y + -0.5) equal to 2.915475947 and -2.915475947.Subproblem 1
y + -0.5 = 2.915475947 Simplifying y + -0.5 = 2.915475947 Reorder the terms: -0.5 + y = 2.915475947 Solving -0.5 + y = 2.915475947 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 = 2.915475947 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = 2.915475947 + 0.5 y = 2.915475947 + 0.5 Combine like terms: 2.915475947 + 0.5 = 3.415475947 y = 3.415475947 Simplifying y = 3.415475947Subproblem 2
y + -0.5 = -2.915475947 Simplifying y + -0.5 = -2.915475947 Reorder the terms: -0.5 + y = -2.915475947 Solving -0.5 + y = -2.915475947 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 = -2.915475947 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = -2.915475947 + 0.5 y = -2.915475947 + 0.5 Combine like terms: -2.915475947 + 0.5 = -2.415475947 y = -2.415475947 Simplifying y = -2.415475947Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.415475947, -2.415475947}
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