4y^2+104y=188

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Solution for 4y^2+104y=188 equation:


Simplifying
4y2 + 104y = 188

Reorder the terms:
104y + 4y2 = 188

Solving
104y + 4y2 = 188

Solving for variable 'y'.

Reorder the terms:
-188 + 104y + 4y2 = 188 + -188

Combine like terms: 188 + -188 = 0
-188 + 104y + 4y2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-47 + 26y + y2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-47 + 26y + y2)' equal to zero and attempt to solve: Simplifying -47 + 26y + y2 = 0 Solving -47 + 26y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + 26y + 47 + y2 = 0 + 47 Reorder the terms: -47 + 47 + 26y + y2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + 26y + y2 = 0 + 47 26y + y2 = 0 + 47 Combine like terms: 0 + 47 = 47 26y + y2 = 47 The y term is 26y. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26y + 169 + y2 = 47 + 169 Reorder the terms: 169 + 26y + y2 = 47 + 169 Combine like terms: 47 + 169 = 216 169 + 26y + y2 = 216 Factor a perfect square on the left side: (y + 13)(y + 13) = 216 Calculate the square root of the right side: 14.696938457 Break this problem into two subproblems by setting (y + 13) equal to 14.696938457 and -14.696938457.

Subproblem 1

y + 13 = 14.696938457 Simplifying y + 13 = 14.696938457 Reorder the terms: 13 + y = 14.696938457 Solving 13 + y = 14.696938457 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + y = 14.696938457 + -13 Combine like terms: 13 + -13 = 0 0 + y = 14.696938457 + -13 y = 14.696938457 + -13 Combine like terms: 14.696938457 + -13 = 1.696938457 y = 1.696938457 Simplifying y = 1.696938457

Subproblem 2

y + 13 = -14.696938457 Simplifying y + 13 = -14.696938457 Reorder the terms: 13 + y = -14.696938457 Solving 13 + y = -14.696938457 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + y = -14.696938457 + -13 Combine like terms: 13 + -13 = 0 0 + y = -14.696938457 + -13 y = -14.696938457 + -13 Combine like terms: -14.696938457 + -13 = -27.696938457 y = -27.696938457 Simplifying y = -27.696938457

Solution

The solution to the problem is based on the solutions from the subproblems. y = {1.696938457, -27.696938457}

Solution

y = {1.696938457, -27.696938457}

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