How do you answer this?

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2 Answers
Jan 31, 2018

Answer:

#x=4+sqrt19# and #x=4-sqrt19#

Explanation:

Using complete the square:

Half term of #x#

#8/2=4x#

Put inside bracket and square it, adding on the constant.

#(x-4)^2-3#

Take away the squared number of the term of #x# in the bracket:

#(x-4)^2-16-3#

Collect like terms

#-16-3=-19#

#(x-4)^2-19#

This is the completed the square format, but now we solve.

#(x-4)^2-19=0#

Add #19#

#(x-4)^2=19#

Get rid of the squared bracket, by square rooting #19#.

Remember the #pm#

#x-4=pmsqrt19#

Add 4

#x=4pmsqrt19#

This means the answer will be either #x=4+sqrt19# and #x=4-sqrt19# as we usually have #2# solutions.

Feb 6, 2018

Answer:

#x=4+-sqrt19#

Explanation:

#"solve using the method of "color(blue)"completing the square"#

#x^2-8x-3=0#

#• " the coefficient of the "x^2" term must be 1 which it is"#

#• " add/subtract "(1/2"coefficient of the x-term")^2" to"#
#x^2-8x#

#x^2+2(-4)xcolor(red)(+16)color(red)(-16)-3=0#

#rArr(x-4)^2-19=0#

#rArr(x-4)^2=19#

#color(blue)"take the square root of both sides"#

#sqrt((x-4)^2)=+-sqrt19larrcolor(blue)"note plus or minus"#

#rArrx-4=+-sqrt19#

#"add 4 to both sides"#

#rArrx=4+-sqrt19larrcolor(red)"exact values"#