# Solve using the Square Root Property 4y^2-12y+3=0 4y2-12y+3=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=4, b=-12, and c=3 into the quadratic formula and solve for y.
12±(-12)2-4⋅(4⋅3)2⋅4
Simplify.
Simplify the numerator.
Raise -12 to the power of 2.
y=12±144-4⋅(4⋅3)2⋅4
Multiply 4 by 3.
y=12±144-4⋅122⋅4
Multiply -4 by 12.
y=12±144-482⋅4
Subtract 48 from 144.
y=12±962⋅4
Rewrite 96 as 42⋅6.
Factor 16 out of 96.
y=12±16(6)2⋅4
Rewrite 16 as 42.
y=12±42⋅62⋅4
y=12±42⋅62⋅4
Pull terms out from under the radical.
y=12±462⋅4
y=12±462⋅4
Multiply 2 by 4.
y=12±468
Simplify 12±468.
y=3±62
y=3±62
Simplify the expression to solve for the + portion of the ±.
Simplify the numerator.
Raise -12 to the power of 2.
y=12±144-4⋅(4⋅3)2⋅4
Multiply 4 by 3.
y=12±144-4⋅122⋅4
Multiply -4 by 12.
y=12±144-482⋅4
Subtract 48 from 144.
y=12±962⋅4
Rewrite 96 as 42⋅6.
Factor 16 out of 96.
y=12±16(6)2⋅4
Rewrite 16 as 42.
y=12±42⋅62⋅4
y=12±42⋅62⋅4
Pull terms out from under the radical.
y=12±462⋅4
y=12±462⋅4
Multiply 2 by 4.
y=12±468
Simplify 12±468.
y=3±62
Change the ± to +.
y=3+62
y=3+62
Simplify the expression to solve for the – portion of the ±.
Simplify the numerator.
Raise -12 to the power of 2.
y=12±144-4⋅(4⋅3)2⋅4
Multiply 4 by 3.
y=12±144-4⋅122⋅4
Multiply -4 by 12.
y=12±144-482⋅4
Subtract 48 from 144.
y=12±962⋅4
Rewrite 96 as 42⋅6.
Factor 16 out of 96.
y=12±16(6)2⋅4
Rewrite 16 as 42.
y=12±42⋅62⋅4
y=12±42⋅62⋅4
Pull terms out from under the radical.
y=12±462⋅4
y=12±462⋅4
Multiply 2 by 4.
y=12±468
Simplify 12±468.
y=3±62
Change the ± to -.
y=3-62
y=3-62
The final answer is the combination of both solutions.
y=3+62,3-62
The result can be shown in multiple forms.
Exact Form:
y=3+62,3-62
Decimal Form:
y=2.72474487…,0.27525512…
Solve using the Square Root Property 4y^2-12y+3=0   ## Download our App from the store

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