9y^2+6y-12=0

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Solution for 9y^2+6y-12=0 equation:


Simplifying
9y2 + 6y + -12 = 0

Reorder the terms:
-12 + 6y + 9y2 = 0

Solving
-12 + 6y + 9y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + 2y + 3y2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-4 + 2y + 3y2)' equal to zero and attempt to solve: Simplifying -4 + 2y + 3y2 = 0 Solving -4 + 2y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.333333333 + 0.6666666667y + y2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + 0.6666666667y + 1.333333333 + y2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + 0.6666666667y + y2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + 0.6666666667y + y2 = 0 + 1.333333333 0.6666666667y + y2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 0.6666666667y + y2 = 1.333333333 The y term is 0.6666666667y. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667y + 0.1111111112 + y2 = 1.333333333 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667y + y2 = 1.333333333 + 0.1111111112 Combine like terms: 1.333333333 + 0.1111111112 = 1.4444444442 0.1111111112 + 0.6666666667y + y2 = 1.4444444442 Factor a perfect square on the left side: (y + 0.3333333334)(y + 0.3333333334) = 1.4444444442 Calculate the square root of the right side: 1.201850425 Break this problem into two subproblems by setting (y + 0.3333333334) equal to 1.201850425 and -1.201850425.

Subproblem 1

y + 0.3333333334 = 1.201850425 Simplifying y + 0.3333333334 = 1.201850425 Reorder the terms: 0.3333333334 + y = 1.201850425 Solving 0.3333333334 + y = 1.201850425 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + y = 1.201850425 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + y = 1.201850425 + -0.3333333334 y = 1.201850425 + -0.3333333334 Combine like terms: 1.201850425 + -0.3333333334 = 0.8685170916 y = 0.8685170916 Simplifying y = 0.8685170916

Subproblem 2

y + 0.3333333334 = -1.201850425 Simplifying y + 0.3333333334 = -1.201850425 Reorder the terms: 0.3333333334 + y = -1.201850425 Solving 0.3333333334 + y = -1.201850425 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + y = -1.201850425 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + y = -1.201850425 + -0.3333333334 y = -1.201850425 + -0.3333333334 Combine like terms: -1.201850425 + -0.3333333334 = -1.5351837584 y = -1.5351837584 Simplifying y = -1.5351837584

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.8685170916, -1.5351837584}

Solution

y = {0.8685170916, -1.5351837584}

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