How do you solve this using the quadratic formula, #x ^ { 2} + 10x = - 25#?

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Answer 1 · 2017-11-18T01:26:36

x = - 5

#x^2 + 10x + 25 = (x + 5)^2#
There is a double root --> x = - 5

Answer 2 · 2017-11-18T03:50:36

#x=-5#

#x^2+10x=-25#

#x^2+10x+25=0#

The general form of a quadratic equation is #ax^2+bx+c#

Comparing, we get

#a=1#
#b=10#
#c=25#
The quadratic formula is, #x=(-b+-sqrt(b^2-4ac))/(2a)#

Plug in the values of #a,b# and #c#

Therefore,

#x=(-10+-sqrt((10)^2-4 xx 1 xx 25))/(2 xx 1)#

#x=(-10+-sqrt(100-100))/2#

#x=(-10+-sqrt0)/2#

#x=(-10)/2#

#x=-5#

As the discriminant was equal to #0#, there is only one root of this quadratic equation.