# Solve using the Square Root Property 7x^2+3x=8

7×2+3x=8
Move 8 to the left side of the equation by subtracting it from both sides.
7×2+3x-8=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=7, b=3, and c=-8 into the quadratic formula and solve for x.
-3±32-4⋅(7⋅-8)2⋅7
Simplify.
Simplify the numerator.
Raise 3 to the power of 2.
x=-3±9-4⋅(7⋅-8)2⋅7
Multiply 7 by -8.
x=-3±9-4⋅-562⋅7
Multiply -4 by -56.
x=-3±9+2242⋅7
x=-3±2332⋅7
x=-3±2332⋅7
Multiply 2 by 7.
x=-3±23314
x=-3±23314
Simplify the expression to solve for the + portion of the ±.
Simplify the numerator.
Raise 3 to the power of 2.
x=-3±9-4⋅(7⋅-8)2⋅7
Multiply 7 by -8.
x=-3±9-4⋅-562⋅7
Multiply -4 by -56.
x=-3±9+2242⋅7
x=-3±2332⋅7
x=-3±2332⋅7
Multiply 2 by 7.
x=-3±23314
Change the ± to +.
x=-3+23314
Rewrite -3 as -1(3).
x=-1⋅3+23314
Factor -1 out of 233.
x=-1⋅3-1(-233)14
Factor -1 out of -1(3)-1(-233).
x=-1(3-233)14
Move the negative in front of the fraction.
x=-3-23314
x=-3-23314
Simplify the expression to solve for the – portion of the ±.
Simplify the numerator.
Raise 3 to the power of 2.
x=-3±9-4⋅(7⋅-8)2⋅7
Multiply 7 by -8.
x=-3±9-4⋅-562⋅7
Multiply -4 by -56.
x=-3±9+2242⋅7
x=-3±2332⋅7
x=-3±2332⋅7
Multiply 2 by 7.
x=-3±23314
Change the ± to -.
x=-3-23314
Rewrite -3 as -1(3).
x=-1⋅3-23314
Factor -1 out of -233.
x=-1⋅3-(233)14
Factor -1 out of -1(3)-(233).
x=-1(3+233)14
Move the negative in front of the fraction.
x=-3+23314
x=-3+23314
The final answer is the combination of both solutions.
x=-3-23314,-3+23314
The result can be shown in multiple forms.
Exact Form:
x=-3-23314,-3+23314
Decimal Form:
x=0.87602410…,-1.30459553…
Solve using the Square Root Property 7x^2+3x=8

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