Question

Solve for Y
116y^2-828y+145=0


Class 10th(Quadratic equation)
By Kavya Meena(Genius) ¡¡¡¡​

Answer 1

Answer:

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Simplifying

=> 116y2 + -348y + 145 = 0

Reorder the terms:

=> 145 + -348y + 116y2 = 0

Solving

=> 145 + -348y + 116y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '29'.

=> 29(5 + -12y + 4y2) = 0

Factor a trinomial.

=> 29((1 + -2y)(5 + -2y)) = 0

Ignore the factor 29.

Subproblem 1

Set the factor '(1 + -2y)' equal to zero and attempt to solve:

Simplifying

=> 1 + -2y = 0

Solving

=> 1 + -2y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-1' to each side of the equation.

=> 1 + -1 + -2y = 0 + -1

Combine like terms: 1 + -1 = 0

=> 0 + -2y = 0 + -1

=> -2y = 0 + -1

Combine like terms: 0 + -1 = -1

=> -2y = -1

Divide each side by '-2'.

==> y = 0.5

Simplifying

==> y = 0.5

Subproblem 2

Set the factor '(5 + -2y)' equal to zero and attempt to solve:

Simplifying

=> 5 + -2y = 0

Solving

=> 5 + -2y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-5' to each side of the equation.

=> 5 + -5 + -2y = 0 + -5

Combine like terms: 5 + -5 = 0

=> 0 + -2y = 0 + -5

=> -2y = 0 + -5

Combine like terms: 0 + -5 = -5

=> -2y = -5

Divide each side by '-2'.

==> y = 2.5

Simplifying

==> y = 2.5

Solution

==> y = {0.5, 2.5}

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