# Solve Using the Square Root Property x^2=7-4x x2=7-4x
Add 4x to both sides of the equation.
x2+4x=7
Move 7 to the left side of the equation by subtracting it from both sides.
x2+4x-7=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=4, and c=-7 into the quadratic formula and solve for x.
-4±42-4⋅(1⋅-7)2⋅1
Simplify.
Simplify the numerator.
Raise 4 to the power of 2.
x=-4±16-4⋅(1⋅-7)2⋅1
Multiply -7 by 1.
x=-4±16-4⋅-72⋅1
Multiply -4 by -7.
x=-4±16+282⋅1
x=-4±442⋅1
Rewrite 44 as 22⋅11.
Factor 4 out of 44.
x=-4±4(11)2⋅1
Rewrite 4 as 22.
x=-4±22⋅112⋅1
x=-4±22⋅112⋅1
Pull terms out from under the radical.
x=-4±2112⋅1
x=-4±2112⋅1
Multiply 2 by 1.
x=-4±2112
Simplify -4±2112.
x=-2±11
x=-2±11
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⋅-7)2⋅1
Multiply -7 by 1.
x=-4±16-4⋅-72⋅1
Multiply -4 by -7.
x=-4±16+282⋅1
x=-4±442⋅1
Rewrite 44 as 22⋅11.
Factor 4 out of 44.
x=-4±4(11)2⋅1
Rewrite 4 as 22.
x=-4±22⋅112⋅1
x=-4±22⋅112⋅1
Pull terms out from under the radical.
x=-4±2112⋅1
x=-4±2112⋅1
Multiply 2 by 1.
x=-4±2112
Simplify -4±2112.
x=-2±11
Change the ± to +.
x=-2+11
x=-2+11
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⋅-7)2⋅1
Multiply -7 by 1.
x=-4±16-4⋅-72⋅1
Multiply -4 by -7.
x=-4±16+282⋅1
x=-4±442⋅1
Rewrite 44 as 22⋅11.
Factor 4 out of 44.
x=-4±4(11)2⋅1
Rewrite 4 as 22.
x=-4±22⋅112⋅1
x=-4±22⋅112⋅1
Pull terms out from under the radical.
x=-4±2112⋅1
x=-4±2112⋅1
Multiply 2 by 1.
x=-4±2112
Simplify -4±2112.
x=-2±11
Change the ± to -.
x=-2-11
x=-2-11
The final answer is the combination of both solutions.
x=-2+11,-2-11
The result can be shown in multiple forms.
Exact Form:
x=-2+11,-2-11
Decimal Form:
x=1.31662479…,-5.31662479…
Solve Using the Square Root Property x^2=7-4x     