Question

If using the method of completing the square to solve the quadratic equation
x2 – 14.0 – 40 = 0, which number would have to be added to "complete the
square"?
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Answer 1

Answer:

89

Step-by-step explanation:

Since $(\frac{-14}{2})^2=49$ and $49-(-40)=49+40=89$, then 89 needs to be added to both sides of the equation to complete the square:

$x^2-14x-40=0\\\\x^2-14x-40+89=0+89\\\\x^2-14x+49=89\\\\(x-7)^2=89\\\\x-7=\pm\sqrt{89}\\\\x=7\pm\sqrt{89}$

By completing the square, we are able to reduce the trinomial into a perfect square binomial, which helps us solve the equation.