5×2+10x-30=0

Factor 5 out of 5×2.

5(x2)+10x-30=0

Factor 5 out of 10x.

5(x2)+5(2x)-30=0

Factor 5 out of -30.

5×2+5(2x)+5⋅-6=0

Factor 5 out of 5×2+5(2x).

5(x2+2x)+5⋅-6=0

Factor 5 out of 5(x2+2x)+5⋅-6.

5(x2+2x-6)=0

5(x2+2x-6)=0

Divide each term in 5(x2+2x-6)=0 by 5.

5(x2+2x-6)5=05

Cancel the common factor of 5.

Cancel the common factor.

5(x2+2x-6)5=05

Divide x2+2x-6 by 1.

x2+2x-6=05

x2+2x-6=05

Divide 0 by 5.

x2+2x-6=0

x2+2x-6=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=1, b=2, and c=-6 into the quadratic formula and solve for x.

-2±22-4⋅(1⋅-6)2⋅1

Simplify the numerator.

Raise 2 to the power of 2.

x=-2±4-4⋅(1⋅-6)2⋅1

Multiply -6 by 1.

x=-2±4-4⋅-62⋅1

Multiply -4 by -6.

x=-2±4+242⋅1

Add 4 and 24.

x=-2±282⋅1

Rewrite 28 as 22⋅7.

Factor 4 out of 28.

x=-2±4(7)2⋅1

Rewrite 4 as 22.

x=-2±22⋅72⋅1

x=-2±22⋅72⋅1

Pull terms out from under the radical.

x=-2±272⋅1

x=-2±272⋅1

Multiply 2 by 1.

x=-2±272

Simplify -2±272.

x=-1±7

x=-1±7

Simplify the numerator.

Raise 2 to the power of 2.

x=-2±4-4⋅(1⋅-6)2⋅1

Multiply -6 by 1.

x=-2±4-4⋅-62⋅1

Multiply -4 by -6.

x=-2±4+242⋅1

Add 4 and 24.

x=-2±282⋅1

Rewrite 28 as 22⋅7.

Factor 4 out of 28.

x=-2±4(7)2⋅1

Rewrite 4 as 22.

x=-2±22⋅72⋅1

x=-2±22⋅72⋅1

Pull terms out from under the radical.

x=-2±272⋅1

x=-2±272⋅1

Multiply 2 by 1.

x=-2±272

Simplify -2±272.

x=-1±7

Change the ± to +.

x=-1+7

x=-1+7

Simplify the numerator.

Raise 2 to the power of 2.

x=-2±4-4⋅(1⋅-6)2⋅1

Multiply -6 by 1.

x=-2±4-4⋅-62⋅1

Multiply -4 by -6.

x=-2±4+242⋅1

Add 4 and 24.

x=-2±282⋅1

Rewrite 28 as 22⋅7.

Factor 4 out of 28.

x=-2±4(7)2⋅1

Rewrite 4 as 22.

x=-2±22⋅72⋅1

x=-2±22⋅72⋅1

Pull terms out from under the radical.

x=-2±272⋅1

x=-2±272⋅1

Multiply 2 by 1.

x=-2±272

Simplify -2±272.

x=-1±7

Change the ± to -.

x=-1-7

x=-1-7

The final answer is the combination of both solutions.

x=-1+7,-1-7

The result can be shown in multiple forms.

Exact Form:

x=-1+7,-1-7

Decimal Form:

x=1.64575131…,-3.64575131…

Solve using the Square Root Property 5x^2+10x-30=0