Answer:
[tex]2\Bigl[(x+\frac{3}{4} )^2-\frac{25}{16} \Bigr][/tex]
Step-by-step explanation:
Step 1
We factor out 2 so that the coefficient of the quadratic term is 1.
[tex]f(x)=2x^2+3x-2\\f(x)=2\bigl(x^2+\frac{3}{2} -1\bigr)[/tex]
Step 2
In this step we add and subtract the square of the coefficient of the x term, this term is [tex]\Bigl(\frac{1}{2} \bigl(\frac{3}{2}\bigr)\Bigr)^2[/tex]. This is the step where we complete the square.
[tex]f(x)=2\Bigl[x^2+\frac{3}{2}x+(\frac{3}{4})^2-(\tfrac{3}{4})^2 -1 \Bigr]\\f(x)=2\Bigl[x^2+\frac{3}{2}x+(\frac{3}{4})^2-\frac{25}{16} \Bigr][/tex]
Step 3
In this step we factor out the perfect square tri-nomial formed by the first 3 terms in last line of step 2. This calculation is shown below,
[tex]f(x)=2\Bigl[\bigl(x+\frac{3}{4} \bigr)^2-\frac{25}{16} \Bigr][/tex]
Answer:
2(x+3/4)^2-25/8
Step-by-step explanation:
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