Question

Solve x2 10x = 24 by completing the square. which is the solution set of the equation?

Answer 1

By completing squares, we will see that the solution set of the quadratic equation is {-12, 2}.

How to complete the square?

Remember the relation:

$(a + b)^2 = a^2 + 2ab + b^2$

Here we start with:

$x^2 + 10x = 24$

Then, we can rewrite it to get:

$x^2 + 2*5*x = 24$

Now we can see that a = x and b = 5, then we can add and subtract 5 squared in the left side, so we get:

$x^2 + 2*5*x + 5^2 - 5^2= 24\\\\(x^2 + 2*5*x + 5^2) - 5^2= 24\\\\(x + 5)^2 = 24 + 25 = 49$

Now we can solve our equation:

$(x + 5)^2 = 49\\x + 5 = \pm \sqrt{49} = \pm 7\\x = -5 \pm 7$

So the solution set is {-12, 2}

If you want to learn more about quadratic equations:

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