4×2-19x+2=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=4, b=-19, and c=2 into the quadratic formula and solve for x.

19±(-19)2-4⋅(4⋅2)2⋅4

Simplify the numerator.

Raise -19 to the power of 2.

x=19±361-4⋅(4⋅2)2⋅4

Multiply 4 by 2.

x=19±361-4⋅82⋅4

Multiply -4 by 8.

x=19±361-322⋅4

Subtract 32 from 361.

x=19±3292⋅4

x=19±3292⋅4

Multiply 2 by 4.

x=19±3298

x=19±3298

Simplify the numerator.

Raise -19 to the power of 2.

x=19±361-4⋅(4⋅2)2⋅4

Multiply 4 by 2.

x=19±361-4⋅82⋅4

Multiply -4 by 8.

x=19±361-322⋅4

Subtract 32 from 361.

x=19±3292⋅4

x=19±3292⋅4

Multiply 2 by 4.

x=19±3298

Change the ± to +.

x=19+3298

x=19+3298

Simplify the numerator.

Raise -19 to the power of 2.

x=19±361-4⋅(4⋅2)2⋅4

Multiply 4 by 2.

x=19±361-4⋅82⋅4

Multiply -4 by 8.

x=19±361-322⋅4

Subtract 32 from 361.

x=19±3292⋅4

x=19±3292⋅4

Multiply 2 by 4.

x=19±3298

Change the ± to -.

x=19-3298

x=19-3298

The final answer is the combination of both solutions.

x=19+3298,19-3298

The result can be shown in multiple forms.

Exact Form:

x=19+3298,19-3298

Decimal Form:

x=4.64229464…,0.10770535…

Solve using the Square Root Property 4x^2-19x+2=0