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 the numerator.

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.

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 numerator.

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.

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 numerator.

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.

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