Question 214986
I need help with sloving quadractic equations by factoring:



{{{-2x^2+13x+7=0}}}


Step 1.  Multiply by -1 to get rid of negative in x-squared term.


{{{2x^2-13x-7=0}}}


Step 2.  We need two integers m an n such that their products is n*m=-2*7=-14 and their sum n+m= -13.


After several tries, these numbers are -14 and 1.


Step 3.  Express -13x as -13x=-14x+1x=-14x+x and replace this in Step 1.


{{{2x^2-13x-7=(2x^2-14x)+(x-7)}}}


Step 4.  Factor out 2x in the first group with parenthesis


{{{2x^2-13x-7=2x(x-7)+1(x-7)}}}


Step 5.  Factor out x-7 common to the groups with parenthesis


{{{2x^2-13x-7=(x-7)(2x+1)=0}}}


Step 6.  The above equation yields two solutions as follows:


{{{x-7=0}}}  and {{{2x+1=0}}}


{{{x=7}}} and  {{{x=-1/2}}}


As a check, let's use the quadratic formula given below and solve


*[invoke quadratic "x", 2, -13, -7 ]


Same result as before.


Step 7.  ANSWER.  The solutions are {{{x=7}}} and {{{x=-1/2}}}


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J