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

0.7×2-2.8x-0.7=0
Factor 0.7 out of 0.7×2-2.8x-0.7.
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 by 0.7 and simplify.
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.
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 expression to solve for the + portion of the ±.
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 expression to solve for the – portion of the ±.
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

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