# Solve Using the Square Root Property x^2-4x-42=0

x2-4x-42=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=-4, and c=-42 into the quadratic formula and solve for x.
4±(-4)2-4⋅(1⋅-42)2⋅1
Simplify.
Simplify the numerator.
Raise -4 to the power of 2.
x=4±16-4⋅(1⋅-42)2⋅1
Multiply -42 by 1.
x=4±16-4⋅-422⋅1
Multiply -4 by -42.
x=4±16+1682⋅1
x=4±1842⋅1
Rewrite 184 as 22⋅46.
Factor 4 out of 184.
x=4±4(46)2⋅1
Rewrite 4 as 22.
x=4±22⋅462⋅1
x=4±22⋅462⋅1
Pull terms out from under the radical.
x=4±2462⋅1
x=4±2462⋅1
Multiply 2 by 1.
x=4±2462
Simplify 4±2462.
x=2±46
x=2±46
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⋅-42)2⋅1
Multiply -42 by 1.
x=4±16-4⋅-422⋅1
Multiply -4 by -42.
x=4±16+1682⋅1
x=4±1842⋅1
Rewrite 184 as 22⋅46.
Factor 4 out of 184.
x=4±4(46)2⋅1
Rewrite 4 as 22.
x=4±22⋅462⋅1
x=4±22⋅462⋅1
Pull terms out from under the radical.
x=4±2462⋅1
x=4±2462⋅1
Multiply 2 by 1.
x=4±2462
Simplify 4±2462.
x=2±46
Change the ± to +.
x=2+46
x=2+46
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⋅-42)2⋅1
Multiply -42 by 1.
x=4±16-4⋅-422⋅1
Multiply -4 by -42.
x=4±16+1682⋅1
x=4±1842⋅1
Rewrite 184 as 22⋅46.
Factor 4 out of 184.
x=4±4(46)2⋅1
Rewrite 4 as 22.
x=4±22⋅462⋅1
x=4±22⋅462⋅1
Pull terms out from under the radical.
x=4±2462⋅1
x=4±2462⋅1
Multiply 2 by 1.
x=4±2462
Simplify 4±2462.
x=2±46
Change the ± to -.
x=2-46
x=2-46
The final answer is the combination of both solutions.
x=2+46,2-46
The result can be shown in multiple forms.
Exact Form:
x=2+46,2-46
Decimal Form:
x=8.78232998…,-4.78232998…
Solve Using the Square Root Property x^2-4x-42=0