Question

Use completing the square to identify the solutions to the quadratic below: d^2 + 4d - 10 = 0

Answer 1

ANSWER

$\begin{gathered} d=-2+\sqrt[]{14} \\ d=-2-\sqrt[]{14} \end{gathered}$

EXPLANATION

We want to solve the quadratic equation using completing the square method:

$d^2+4d-10=0$

The general form of a quadratic equation is:

$ax^2+bx+c=0$

where a, b and c are coefficients.

The first step is to find a number that is equal to:

$(\frac{b}{2})^2$

From the given equation, b is 4.

So, we have that:

$(\frac{4}{2})^2=2^2=4$

Now, we can add that number to both sides of the equation and write it in this form:

$(d^2+4d+4)-10=4$

Factorize the part of the left hand side in the parantheses:

$\begin{gathered} (d^2+2d+2d+4)-10=4 \\ (d+2)^2-10=4 \end{gathered}$

Add 10 to both sides of the equation:

$\begin{gathered} (d+2)^2=4+10 \\ (d+2)^2=14 \end{gathered}$

Find the square root of both sides:

$\begin{gathered} d+2=+\sqrt[]{14} \\ \text{and} \\ d+2=-\sqrt[]{14} \end{gathered}$

Subtract 2 from both sides of the equation:

$\begin{gathered} \Rightarrow d=-2+\sqrt[]{14} \\ \text{and} \\ \Rightarrow d=-2-\sqrt[]{14} \end{gathered}$

That is the solution of the equation according to completing the square method.