0.7×2-2.8x-0.7=0

Factor 0.7 out of 0.7×2.

0.7(x2)-2.8x-0.7=0

Factor 0.7 out of -2.8x.

0.7(x2)+0.7(-4x)-0.7=0

Factor 0.7 out of -0.7.

0.7(x2)+0.7(-4x)+0.7(-1)=0

Factor 0.7 out of 0.7(x2)+0.7(-4x).

0.7(x2-4x)+0.7(-1)=0

Factor 0.7 out of 0.7(x2-4x)+0.7(-1).

0.7(x2-4x-1)=0

0.7(x2-4x-1)=0

Divide each term in 0.7(x2-4x-1)=0 by 0.7.

0.7(x2-4x-1)0.7=00.7

Cancel the common factor of 0.7.

x2-4x-1=00.7

Divide 0 by 0.7.

x2-4x-1=0

x2-4x-1=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=1, b=-4, and c=-1 into the quadratic formula and solve for x.

4±(-4)2-4⋅(1⋅-1)2⋅1

Simplify the numerator.

Raise -4 to the power of 2.

x=4±16-4⋅(1⋅-1)2⋅1

Multiply -1 by 1.

x=4±16-4⋅-12⋅1

Multiply -4 by -1.

x=4±16+42⋅1

Add 16 and 4.

x=4±202⋅1

Rewrite 20 as 22⋅5.

Factor 4 out of 20.

x=4±4(5)2⋅1

Rewrite 4 as 22.

x=4±22⋅52⋅1

x=4±22⋅52⋅1

Pull terms out from under the radical.

x=4±252⋅1

x=4±252⋅1

Multiply 2 by 1.

x=4±252

Simplify 4±252.

x=2±5

x=2±5

Simplify the numerator.

Raise -4 to the power of 2.

x=4±16-4⋅(1⋅-1)2⋅1

Multiply -1 by 1.

x=4±16-4⋅-12⋅1

Multiply -4 by -1.

x=4±16+42⋅1

Add 16 and 4.

x=4±202⋅1

Rewrite 20 as 22⋅5.

Factor 4 out of 20.

x=4±4(5)2⋅1

Rewrite 4 as 22.

x=4±22⋅52⋅1

x=4±22⋅52⋅1

Pull terms out from under the radical.

x=4±252⋅1

x=4±252⋅1

Multiply 2 by 1.

x=4±252

Simplify 4±252.

x=2±5

Change the ± to +.

x=2+5

x=2+5

Simplify the numerator.

Raise -4 to the power of 2.

x=4±16-4⋅(1⋅-1)2⋅1

Multiply -1 by 1.

x=4±16-4⋅-12⋅1

Multiply -4 by -1.

x=4±16+42⋅1

Add 16 and 4.

x=4±202⋅1

Rewrite 20 as 22⋅5.

Factor 4 out of 20.

x=4±4(5)2⋅1

Rewrite 4 as 22.

x=4±22⋅52⋅1

x=4±22⋅52⋅1

Pull terms out from under the radical.

x=4±252⋅1

x=4±252⋅1

Multiply 2 by 1.

x=4±252

Simplify 4±252.

x=2±5

Change the ± to -.

x=2-5

x=2-5

The final answer is the combination of both solutions.

x=2+5,2-5

The result can be shown in multiple forms.

Exact Form:

x=2+5,2-5

Decimal Form:

x=4.23606797…,-0.23606797…

Solve Using the Square Root Property 0.7x^2-2.8x-0.7=0