# Solve Using the Square Root Property 5x^2-7x=16

5×2-7x=16
Move 16 to the left side of the equation by subtracting it from both sides.
5×2-7x-16=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=5, b=-7, and c=-16 into the quadratic formula and solve for x.
7±(-7)2-4⋅(5⋅-16)2⋅5
Simplify.
Simplify the numerator.
Raise -7 to the power of 2.
x=7±49-4⋅(5⋅-16)2⋅5
Multiply 5 by -16.
x=7±49-4⋅-802⋅5
Multiply -4 by -80.
x=7±49+3202⋅5
Add 49 and 320.
x=7±3692⋅5
Rewrite 369 as 32⋅41.
Factor 9 out of 369.
x=7±9(41)2⋅5
Rewrite 9 as 32.
x=7±32⋅412⋅5
x=7±32⋅412⋅5
Pull terms out from under the radical.
x=7±3412⋅5
x=7±3412⋅5
Multiply 2 by 5.
x=7±34110
x=7±34110
Simplify the expression to solve for the + portion of the ±.
Simplify the numerator.
Raise -7 to the power of 2.
x=7±49-4⋅(5⋅-16)2⋅5
Multiply 5 by -16.
x=7±49-4⋅-802⋅5
Multiply -4 by -80.
x=7±49+3202⋅5
Add 49 and 320.
x=7±3692⋅5
Rewrite 369 as 32⋅41.
Factor 9 out of 369.
x=7±9(41)2⋅5
Rewrite 9 as 32.
x=7±32⋅412⋅5
x=7±32⋅412⋅5
Pull terms out from under the radical.
x=7±3412⋅5
x=7±3412⋅5
Multiply 2 by 5.
x=7±34110
Change the ± to +.
x=7+34110
x=7+34110
Simplify the expression to solve for the – portion of the ±.
Simplify the numerator.
Raise -7 to the power of 2.
x=7±49-4⋅(5⋅-16)2⋅5
Multiply 5 by -16.
x=7±49-4⋅-802⋅5
Multiply -4 by -80.
x=7±49+3202⋅5
Add 49 and 320.
x=7±3692⋅5
Rewrite 369 as 32⋅41.
Factor 9 out of 369.
x=7±9(41)2⋅5
Rewrite 9 as 32.
x=7±32⋅412⋅5
x=7±32⋅412⋅5
Pull terms out from under the radical.
x=7±3412⋅5
x=7±3412⋅5
Multiply 2 by 5.
x=7±34110
Change the ± to -.
x=7-34110
x=7-34110
The final answer is the combination of both solutions.
x=7+34110,7-34110
The result can be shown in multiple forms.
Exact Form:
x=7+34110,7-34110
Decimal Form:
x=2.62093727…,-1.22093727…
Solve Using the Square Root Property 5x^2-7x=16

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