# Solve Using the Square Root Property 2x^2+5x-1=0 2×2+5x-1=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=2, b=5, and c=-1 into the quadratic formula and solve for x.
-5±52-4⋅(2⋅-1)2⋅2
Simplify.
Simplify the numerator.
Raise 5 to the power of 2.
x=-5±25-4⋅(2⋅-1)2⋅2
Multiply 2 by -1.
x=-5±25-4⋅-22⋅2
Multiply -4 by -2.
x=-5±25+82⋅2
Add 25 and 8.
x=-5±332⋅2
x=-5±332⋅2
Multiply 2 by 2.
x=-5±334
x=-5±334
Simplify the expression to solve for the + portion of the ±.
Simplify the numerator.
Raise 5 to the power of 2.
x=-5±25-4⋅(2⋅-1)2⋅2
Multiply 2 by -1.
x=-5±25-4⋅-22⋅2
Multiply -4 by -2.
x=-5±25+82⋅2
Add 25 and 8.
x=-5±332⋅2
x=-5±332⋅2
Multiply 2 by 2.
x=-5±334
Change the ± to +.
x=-5+334
Rewrite -5 as -1(5).
x=-1⋅5+334
Factor -1 out of 33.
x=-1⋅5-1(-33)4
Factor -1 out of -1(5)-1(-33).
x=-1(5-33)4
Move the negative in front of the fraction.
x=-5-334
x=-5-334
Simplify the expression to solve for the – portion of the ±.
Simplify the numerator.
Raise 5 to the power of 2.
x=-5±25-4⋅(2⋅-1)2⋅2
Multiply 2 by -1.
x=-5±25-4⋅-22⋅2
Multiply -4 by -2.
x=-5±25+82⋅2
Add 25 and 8.
x=-5±332⋅2
x=-5±332⋅2
Multiply 2 by 2.
x=-5±334
Change the ± to -.
x=-5-334
Rewrite -5 as -1(5).
x=-1⋅5-334
Factor -1 out of -33.
x=-1⋅5-(33)4
Factor -1 out of -1(5)-(33).
x=-1(5+33)4
Move the negative in front of the fraction.
x=-5+334
x=-5+334
The final answer is the combination of both solutions.
x=-5-334,-5+334
The result can be shown in multiple forms.
Exact Form:
x=-5-334,-5+334
Decimal Form:
x=0.18614066…,-2.68614066…
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