Answer:
[tex]x^2+15x+\boxed{\dfrac{225}{4}}=\boxed{\dfrac{421}{4}}[/tex]
[tex]x^2+15x+\boxed{56.25}=\boxed{105.25}[/tex]
Step-by-step explanation:
General form of a quadratic equation: [tex]ax^2+bx+c[/tex]
When completing the square, first add the number that is the square of half of [tex]b[/tex].
Given equation: [tex]x^2+15x=49[/tex]
Therefore, [tex]b=15[/tex]
[tex]\implies \left(\dfrac{b}{2}\right)^2=\left(\dfrac{15}{2}\right)^2=\dfrac{225}{4}[/tex]
So we need to add 225/4 to both sides of the equation:
[tex]\implies x^2+15x+\dfrac{225}{4}=49+\dfrac{225}{4}[/tex]
[tex]\implies x^2+15x+\boxed{\dfrac{225}{4}}=\boxed{\dfrac{421}{4}}[/tex]
In decimal form:
[tex]\implies x^2+15x+\boxed{56.25}=\boxed{105.25}[/tex]
To finish completing the square,
factor the left side of the equation:
[tex]\implies \left(x+\dfrac{15}{2}\right)^2=\dfrac{421}{4}[/tex]
Finally, subtract 421/4 from both sides:
[tex]\implies \left(x+\dfrac{15}{2}\right)^2-\dfrac{421}{4}=0[/tex]
In decimal form:
[tex]\implies (x+7.5)^2-105.25=0[/tex]
