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

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.
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 expression to solve for the + portion of the ±.
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 expression to solve for the – portion of the ±.
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