How do you solve using the completing the square method $x^{2} - 30 x = - 125$ $x^2 - 30x = -125$ ?

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How do you solve using the completing the square method $x^{2} - 30 x = - 125$ $x^2 - 30x = -125$ ?

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Answer 1 · 2016-03-20T17:53:37

$x = 5 or x = 25$ $x=5 or x=25$

Explanation:

One usually starts by dividing throughout by the coefficient of $x^{2}$ $x^2$ and taking all $x$ $x$ terms to one side. The given equation is already in this format.

Next step, take the coefficient of $x$ $x$ , half it, square it, and add it to both sides.

$therefore x^2-30x+(-30/2)^2=-125+(-30/2)^2$

Now write the left hand side as a perfect square and simplify the right hand side.

$therefore (x-15)^2=-125+900/4=100$

Now take the square root on both sides and solve for $x$

$therefore x-15=+-sqrt100=+-10$

$therefore x=15+-10$

$=25 or 5$

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How do you solve using the completing the square method $x^{2} - 30 x = - 125$ $x^2 - 30x = -125$ ?

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Explanation:

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How do you solve using the completing the square method $x^{2} - 30 x = - 125$ $x^2 - 30x = -125$ ?