# Solve Using the Square Root Property 9(680/40)+6x^2=89 9(68040)+6×2=89
Simplify each term.
Divide 680 by 40.
9⋅17+6×2=89
Multiply 9 by 17.
153+6×2=89
153+6×2=89
Move all terms not containing x to the right side of the equation.
Subtract 153 from both sides of the equation.
6×2=89-153
Subtract 153 from 89.
6×2=-64
6×2=-64
Divide each term by 6 and simplify.
Divide each term in 6×2=-64 by 6.
6×26=-646
Cancel the common factor of 6.
Cancel the common factor.
6×26=-646
Divide x2 by 1.
x2=-646
x2=-646
Simplify -646.
Cancel the common factor of -64 and 6.
Factor 2 out of -64.
x2=2(-32)6
Cancel the common factors.
Factor 2 out of 6.
x2=2⋅-322⋅3
Cancel the common factor.
x2=2⋅-322⋅3
Rewrite the expression.
x2=-323
x2=-323
x2=-323
Move the negative in front of the fraction.
x2=-323
x2=-323
x2=-323
Take the square root of both sides of the equation to eliminate the exponent on the left side.
x=±-323
The complete solution is the result of both the positive and negative portions of the solution.
Simplify the right side of the equation.
Rewrite -1 as i2.
x=±i2(323)
Pull terms out from under the radical.
x=±i323
Rewrite 323 as 323.
x=±i(323)
Simplify the numerator.
Rewrite 32 as 42⋅2.
Factor 16 out of 32.
x=±i(16(2)3)
Rewrite 16 as 42.
x=±i(42⋅23)
x=±i(42⋅23)
Pull terms out from under the radical.
x=±i(423)
x=±i(423)
Multiply 423 by 33.
x=±i(423⋅33)
Combine and simplify the denominator.
Multiply 423 and 33.
x=±i(42333)
Raise 3 to the power of 1.
x=±i(42333)
Raise 3 to the power of 1.
x=±i(42333)
Use the power rule aman=am+n to combine exponents.
x=±i(42331+1)
x=±i(42332)
Rewrite 32 as 3.
Use axn=axn to rewrite 3 as 312.
x=±i(423(312)2)
Apply the power rule and multiply exponents, (am)n=amn.
x=±i(423312⋅2)
Combine 12 and 2.
x=±i(423322)
Cancel the common factor of 2.
Cancel the common factor.
x=±i(423322)
Divide 1 by 1.
x=±i(4233)
x=±i(4233)
Evaluate the exponent.
x=±i(4233)
x=±i(4233)
x=±i(4233)
Simplify the numerator.
Combine using the product rule for radicals.
x=±i(43⋅23)
Multiply 3 by 2.
x=±i(463)
x=±i(463)
Combine fractions.
Combine i and 463.
x=±i(46)3
Move 4 to the left of i.
x=±4i63
x=±4i63
x=±4i63
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the ± to find the first solution.
x=4i63
Next, use the negative value of the ± to find the second solution.
x=-4i63
The complete solution is the result of both the positive and negative portions of the solution.
x=4i63,-4i63
x=4i63,-4i63
x=4i63,-4i63
Solve Using the Square Root Property 9(680/40)+6x^2=89     