Solve using the Square Root Property 5x^2+12x+6=0

Math
5×2+12x+6=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=5, b=12, and c=6 into the quadratic formula and solve for x.
-12±122-4⋅(5⋅6)2⋅5
Simplify.
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Simplify the numerator.
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Raise 12 to the power of 2.
x=-12±144-4⋅(5⋅6)2⋅5
Multiply 5 by 6.
x=-12±144-4⋅302⋅5
Multiply -4 by 30.
x=-12±144-1202⋅5
Subtract 120 from 144.
x=-12±242⋅5
Rewrite 24 as 22⋅6.
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Factor 4 out of 24.
x=-12±4(6)2⋅5
Rewrite 4 as 22.
x=-12±22⋅62⋅5
x=-12±22⋅62⋅5
Pull terms out from under the radical.
x=-12±262⋅5
x=-12±262⋅5
Multiply 2 by 5.
x=-12±2610
Simplify -12±2610.
x=-6±65
x=-6±65
Simplify the expression to solve for the + portion of the ±.
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Simplify the numerator.
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Raise 12 to the power of 2.
x=-12±144-4⋅(5⋅6)2⋅5
Multiply 5 by 6.
x=-12±144-4⋅302⋅5
Multiply -4 by 30.
x=-12±144-1202⋅5
Subtract 120 from 144.
x=-12±242⋅5
Rewrite 24 as 22⋅6.
Tap for more steps…
Factor 4 out of 24.
x=-12±4(6)2⋅5
Rewrite 4 as 22.
x=-12±22⋅62⋅5
x=-12±22⋅62⋅5
Pull terms out from under the radical.
x=-12±262⋅5
x=-12±262⋅5
Multiply 2 by 5.
x=-12±2610
Simplify -12±2610.
x=-6±65
Change the ± to +.
x=-6+65
Rewrite -6 as -1(6).
x=-1⋅6+65
Factor -1 out of 6.
x=-1⋅6-1(-6)5
Factor -1 out of -1(6)-1(-6).
x=-1(6-6)5
Move the negative in front of the fraction.
x=-6-65
x=-6-65
Simplify the expression to solve for the – portion of the ±.
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Simplify the numerator.
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Raise 12 to the power of 2.
x=-12±144-4⋅(5⋅6)2⋅5
Multiply 5 by 6.
x=-12±144-4⋅302⋅5
Multiply -4 by 30.
x=-12±144-1202⋅5
Subtract 120 from 144.
x=-12±242⋅5
Rewrite 24 as 22⋅6.
Tap for more steps…
Factor 4 out of 24.
x=-12±4(6)2⋅5
Rewrite 4 as 22.
x=-12±22⋅62⋅5
x=-12±22⋅62⋅5
Pull terms out from under the radical.
x=-12±262⋅5
x=-12±262⋅5
Multiply 2 by 5.
x=-12±2610
Simplify -12±2610.
x=-6±65
Change the ± to -.
x=-6-65
Rewrite -6 as -1(6).
x=-1⋅6-65
Factor -1 out of -6.
x=-1⋅6-(6)5
Factor -1 out of -1(6)-(6).
x=-1(6+6)5
Move the negative in front of the fraction.
x=-6+65
x=-6+65
The final answer is the combination of both solutions.
x=-6-65,-6+65
The result can be shown in multiple forms.
Exact Form:
x=-6-65,-6+65
Decimal Form:
x=-0.71010205…,-1.68989794…
Solve using the Square Root Property 5x^2+12x+6=0

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