# Solve using the Square Root Property m^2-1=-7m

m2-1=-7m
Add 7m to both sides of the equation.
m2-1+7m=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=7, and c=-1 into the quadratic formula and solve for m.
-7±72-4⋅(1⋅-1)2⋅1
Simplify.
Simplify the numerator.
Raise 7 to the power of 2.
m=-7±49-4⋅(1⋅-1)2⋅1
Multiply -1 by 1.
m=-7±49-4⋅-12⋅1
Multiply -4 by -1.
m=-7±49+42⋅1
m=-7±532⋅1
m=-7±532⋅1
Multiply 2 by 1.
m=-7±532
m=-7±532
Simplify the expression to solve for the + portion of the ±.
Simplify the numerator.
Raise 7 to the power of 2.
m=-7±49-4⋅(1⋅-1)2⋅1
Multiply -1 by 1.
m=-7±49-4⋅-12⋅1
Multiply -4 by -1.
m=-7±49+42⋅1
m=-7±532⋅1
m=-7±532⋅1
Multiply 2 by 1.
m=-7±532
Change the ± to +.
m=-7+532
Rewrite -7 as -1(7).
m=-1⋅7+532
Factor -1 out of 53.
m=-1⋅7-1(-53)2
Factor -1 out of -1(7)-1(-53).
m=-1(7-53)2
Move the negative in front of the fraction.
m=-7-532
m=-7-532
Simplify the expression to solve for the – portion of the ±.
Simplify the numerator.
Raise 7 to the power of 2.
m=-7±49-4⋅(1⋅-1)2⋅1
Multiply -1 by 1.
m=-7±49-4⋅-12⋅1
Multiply -4 by -1.
m=-7±49+42⋅1
m=-7±532⋅1
m=-7±532⋅1
Multiply 2 by 1.
m=-7±532
Change the ± to -.
m=-7-532
Rewrite -7 as -1(7).
m=-1⋅7-532
Factor -1 out of -53.
m=-1⋅7-(53)2
Factor -1 out of -1(7)-(53).
m=-1(7+53)2
Move the negative in front of the fraction.
m=-7+532
m=-7+532
The final answer is the combination of both solutions.
m=-7-532,-7+532
The result can be shown in multiple forms.
Exact Form:
m=-7-532,-7+532
Decimal Form:
m=0.14005494…,-7.14005494…
Solve using the Square Root Property m^2-1=-7m