# Solve Using the Square Root Property 2x^2+3x-4=0

2×2+3x-4=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=2, b=3, and c=-4 into the quadratic formula and solve for x.
-3±32-4⋅(2⋅-4)2⋅2
Simplify.
Simplify the numerator.
Raise 3 to the power of 2.
x=-3±9-4⋅(2⋅-4)2⋅2
Multiply 2 by -4.
x=-3±9-4⋅-82⋅2
Multiply -4 by -8.
x=-3±9+322⋅2
x=-3±412⋅2
x=-3±412⋅2
Multiply 2 by 2.
x=-3±414
x=-3±414
Simplify the expression to solve for the + portion of the ±.
Simplify the numerator.
Raise 3 to the power of 2.
x=-3±9-4⋅(2⋅-4)2⋅2
Multiply 2 by -4.
x=-3±9-4⋅-82⋅2
Multiply -4 by -8.
x=-3±9+322⋅2
x=-3±412⋅2
x=-3±412⋅2
Multiply 2 by 2.
x=-3±414
Change the ± to +.
x=-3+414
Rewrite -3 as -1(3).
x=-1⋅3+414
Factor -1 out of 41.
x=-1⋅3-1(-41)4
Factor -1 out of -1(3)-1(-41).
x=-1(3-41)4
Move the negative in front of the fraction.
x=-3-414
x=-3-414
Simplify the expression to solve for the – portion of the ±.
Simplify the numerator.
Raise 3 to the power of 2.
x=-3±9-4⋅(2⋅-4)2⋅2
Multiply 2 by -4.
x=-3±9-4⋅-82⋅2
Multiply -4 by -8.
x=-3±9+322⋅2
x=-3±412⋅2
x=-3±412⋅2
Multiply 2 by 2.
x=-3±414
Change the ± to -.
x=-3-414
Rewrite -3 as -1(3).
x=-1⋅3-414
Factor -1 out of -41.
x=-1⋅3-(41)4
Factor -1 out of -1(3)-(41).
x=-1(3+41)4
Move the negative in front of the fraction.
x=-3+414
x=-3+414
The final answer is the combination of both solutions.
x=-3-414,-3+414
The result can be shown in multiple forms.
Exact Form:
x=-3-414,-3+414
Decimal Form:
x=0.85078105…,-2.35078105…
Solve Using the Square Root Property 2x^2+3x-4=0