Solve Using the Square Root Property 3x^2-14x+23=0

Math
3×2-14x+23=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=3, b=-14, and c=23 into the quadratic formula and solve for x.
14±(-14)2-4⋅(3⋅23)2⋅3
Simplify.
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Simplify the numerator.
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Raise -14 to the power of 2.
x=14±196-4⋅(3⋅23)2⋅3
Multiply 3 by 23.
x=14±196-4⋅692⋅3
Multiply -4 by 69.
x=14±196-2762⋅3
Subtract 276 from 196.
x=14±-802⋅3
Rewrite -80 as -1(80).
x=14±-1⋅802⋅3
Rewrite -1(80) as -1⋅80.
x=14±-1⋅802⋅3
Rewrite -1 as i.
x=14±i⋅802⋅3
Rewrite 80 as 42⋅5.
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Factor 16 out of 80.
x=14±i⋅16(5)2⋅3
Rewrite 16 as 42.
x=14±i⋅42⋅52⋅3
x=14±i⋅42⋅52⋅3
Pull terms out from under the radical.
x=14±i⋅(45)2⋅3
Move 4 to the left of i.
x=14±4i52⋅3
x=14±4i52⋅3
Multiply 2 by 3.
x=14±4i56
Simplify 14±4i56.
x=7±2i53
x=7±2i53
Simplify the expression to solve for the + portion of the ±.
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Simplify the numerator.
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Raise -14 to the power of 2.
x=14±196-4⋅(3⋅23)2⋅3
Multiply 3 by 23.
x=14±196-4⋅692⋅3
Multiply -4 by 69.
x=14±196-2762⋅3
Subtract 276 from 196.
x=14±-802⋅3
Rewrite -80 as -1(80).
x=14±-1⋅802⋅3
Rewrite -1(80) as -1⋅80.
x=14±-1⋅802⋅3
Rewrite -1 as i.
x=14±i⋅802⋅3
Rewrite 80 as 42⋅5.
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Factor 16 out of 80.
x=14±i⋅16(5)2⋅3
Rewrite 16 as 42.
x=14±i⋅42⋅52⋅3
x=14±i⋅42⋅52⋅3
Pull terms out from under the radical.
x=14±i⋅(45)2⋅3
Move 4 to the left of i.
x=14±4i52⋅3
x=14±4i52⋅3
Multiply 2 by 3.
x=14±4i56
Simplify 14±4i56.
x=7±2i53
Change the ± to +.
x=7+2i53
x=7+2i53
Simplify the expression to solve for the – portion of the ±.
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Simplify the numerator.
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Raise -14 to the power of 2.
x=14±196-4⋅(3⋅23)2⋅3
Multiply 3 by 23.
x=14±196-4⋅692⋅3
Multiply -4 by 69.
x=14±196-2762⋅3
Subtract 276 from 196.
x=14±-802⋅3
Rewrite -80 as -1(80).
x=14±-1⋅802⋅3
Rewrite -1(80) as -1⋅80.
x=14±-1⋅802⋅3
Rewrite -1 as i.
x=14±i⋅802⋅3
Rewrite 80 as 42⋅5.
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Factor 16 out of 80.
x=14±i⋅16(5)2⋅3
Rewrite 16 as 42.
x=14±i⋅42⋅52⋅3
x=14±i⋅42⋅52⋅3
Pull terms out from under the radical.
x=14±i⋅(45)2⋅3
Move 4 to the left of i.
x=14±4i52⋅3
x=14±4i52⋅3
Multiply 2 by 3.
x=14±4i56
Simplify 14±4i56.
x=7±2i53
Change the ± to -.
x=7-2i53
x=7-2i53
The final answer is the combination of both solutions.
x=7+2i53,7-2i53
Solve Using the Square Root Property 3x^2-14x+23=0

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