# Solve Using the Square Root Property 5x^2- square root of 3x-2=0 5×2-3x-2=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=5, b=-3, and c=-2 into the quadratic formula and solve for x.
3±(-3)2-4⋅(5⋅-2)2⋅5
Simplify.
Simplify the numerator.
Apply the product rule to -3.
x=3±(-1)232-4⋅(5⋅-2)2⋅5
Raise -1 to the power of 2.
x=3±132-4⋅(5⋅-2)2⋅5
Multiply 32 by 1.
x=3±32-4⋅(5⋅-2)2⋅5
Rewrite 32 as 3.
Use axn=axn to rewrite 3 as 312.
x=3±(312)2-4⋅(5⋅-2)2⋅5
Apply the power rule and multiply exponents, (am)n=amn.
x=3±312⋅2-4⋅(5⋅-2)2⋅5
Combine 12 and 2.
x=3±322-4⋅(5⋅-2)2⋅5
Cancel the common factor of 2.
Cancel the common factor.
x=3±322-4⋅(5⋅-2)2⋅5
Divide 1 by 1.
x=3±3-4⋅(5⋅-2)2⋅5
x=3±3-4⋅(5⋅-2)2⋅5
Evaluate the exponent.
x=3±3-4⋅(5⋅-2)2⋅5
x=3±3-4⋅(5⋅-2)2⋅5
Multiply 5 by -2.
x=3±3-4⋅-102⋅5
Multiply -4 by -10.
x=3±3+402⋅5
x=3±432⋅5
x=3±432⋅5
Multiply 2 by 5.
x=3±4310
x=3±4310
Simplify the expression to solve for the + portion of the ±.
Simplify the numerator.
Apply the product rule to -3.
x=3±(-1)232-4⋅(5⋅-2)2⋅5
Raise -1 to the power of 2.
x=3±132-4⋅(5⋅-2)2⋅5
Multiply 32 by 1.
x=3±32-4⋅(5⋅-2)2⋅5
Rewrite 32 as 3.
Use axn=axn to rewrite 3 as 312.
x=3±(312)2-4⋅(5⋅-2)2⋅5
Apply the power rule and multiply exponents, (am)n=amn.
x=3±312⋅2-4⋅(5⋅-2)2⋅5
Combine 12 and 2.
x=3±322-4⋅(5⋅-2)2⋅5
Cancel the common factor of 2.
Cancel the common factor.
x=3±322-4⋅(5⋅-2)2⋅5
Divide 1 by 1.
x=3±3-4⋅(5⋅-2)2⋅5
x=3±3-4⋅(5⋅-2)2⋅5
Evaluate the exponent.
x=3±3-4⋅(5⋅-2)2⋅5
x=3±3-4⋅(5⋅-2)2⋅5
Multiply 5 by -2.
x=3±3-4⋅-102⋅5
Multiply -4 by -10.
x=3±3+402⋅5
x=3±432⋅5
x=3±432⋅5
Multiply 2 by 5.
x=3±4310
Change the ± to +.
x=3+4310
x=3+4310
Simplify the expression to solve for the – portion of the ±.
Simplify the numerator.
Apply the product rule to -3.
x=3±(-1)232-4⋅(5⋅-2)2⋅5
Raise -1 to the power of 2.
x=3±132-4⋅(5⋅-2)2⋅5
Multiply 32 by 1.
x=3±32-4⋅(5⋅-2)2⋅5
Rewrite 32 as 3.
Use axn=axn to rewrite 3 as 312.
x=3±(312)2-4⋅(5⋅-2)2⋅5
Apply the power rule and multiply exponents, (am)n=amn.
x=3±312⋅2-4⋅(5⋅-2)2⋅5
Combine 12 and 2.
x=3±322-4⋅(5⋅-2)2⋅5
Cancel the common factor of 2.
Cancel the common factor.
x=3±322-4⋅(5⋅-2)2⋅5
Divide 1 by 1.
x=3±3-4⋅(5⋅-2)2⋅5
x=3±3-4⋅(5⋅-2)2⋅5
Evaluate the exponent.
x=3±3-4⋅(5⋅-2)2⋅5
x=3±3-4⋅(5⋅-2)2⋅5
Multiply 5 by -2.
x=3±3-4⋅-102⋅5
Multiply -4 by -10.
x=3±3+402⋅5
x=3±432⋅5
x=3±432⋅5
Multiply 2 by 5.
x=3±4310
Change the ± to -.
x=3-4310
x=3-4310
The final answer is the combination of both solutions.
x=3+4310,3-4310
The result can be shown in multiple forms.
Exact Form:
x=3+4310,3-4310
Decimal Form:
x=0.82894893…,-0.48253877…
Solve Using the Square Root Property 5x^2- square root of 3x-2=0     