4y^2+22y=10

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Solution for 4y^2+22y=10 equation:


Simplifying
4y2 + 22y = 10

Reorder the terms:
22y + 4y2 = 10

Solving
22y + 4y2 = 10

Solving for variable 'y'.

Reorder the terms:
-10 + 22y + 4y2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 22y + 4y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 11y + 2y2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-5 + 11y + 2y2)' equal to zero and attempt to solve: Simplifying -5 + 11y + 2y2 = 0 Solving -5 + 11y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + 5.5y + y2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 5.5y + 2.5 + y2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 5.5y + y2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 5.5y + y2 = 0 + 2.5 5.5y + y2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 5.5y + y2 = 2.5 The y term is 5.5y. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5y + 7.5625 + y2 = 2.5 + 7.5625 Reorder the terms: 7.5625 + 5.5y + y2 = 2.5 + 7.5625 Combine like terms: 2.5 + 7.5625 = 10.0625 7.5625 + 5.5y + y2 = 10.0625 Factor a perfect square on the left side: (y + 2.75)(y + 2.75) = 10.0625 Calculate the square root of the right side: 3.172144385 Break this problem into two subproblems by setting (y + 2.75) equal to 3.172144385 and -3.172144385.

Subproblem 1

y + 2.75 = 3.172144385 Simplifying y + 2.75 = 3.172144385 Reorder the terms: 2.75 + y = 3.172144385 Solving 2.75 + y = 3.172144385 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + y = 3.172144385 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + y = 3.172144385 + -2.75 y = 3.172144385 + -2.75 Combine like terms: 3.172144385 + -2.75 = 0.422144385 y = 0.422144385 Simplifying y = 0.422144385

Subproblem 2

y + 2.75 = -3.172144385 Simplifying y + 2.75 = -3.172144385 Reorder the terms: 2.75 + y = -3.172144385 Solving 2.75 + y = -3.172144385 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + y = -3.172144385 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + y = -3.172144385 + -2.75 y = -3.172144385 + -2.75 Combine like terms: -3.172144385 + -2.75 = -5.922144385 y = -5.922144385 Simplifying y = -5.922144385

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.422144385, -5.922144385}

Solution

y = {0.422144385, -5.922144385}

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