Question

Math

Posted 6 months ago

```
Rewrite the equation by completing the square.
$\begin{array}{l}
x^{2}-16 x+63=0 \\
(x+\square)^{2}=\square
\end{array}$
```

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Answer from Sia

Posted 6 months ago

Solution by Steps

step 1

To complete the square for the equation $x^2 - 16x + 63 = 0$, we first need to find the number that will make $x^2 - 16x$ a perfect square trinomial

step 2

The coefficient of $x$ is $-16$, so we take half of that number, which is $-8$, and then square it to get $64$

step 3

We add and subtract $64$ inside the equation to maintain equality. The equation becomes $x^2 - 16x + 64 - 64 + 63 = 0$

step 4

Grouping the perfect square trinomial together and combining the constants, we have $(x - 8)^2 - 1 = 0$

step 5

Adding $1$ to both sides to isolate the perfect square, we get $(x - 8)^2 = 1$

step 6

Taking the square root of both sides, we find that $x - 8 = \pm 1$

step 7

Solving for $x$, we get two solutions: $x = 8 + 1$ and $x = 8 - 1$

step 8

Therefore, the solutions are $x = 9$ and $x = 7$

Answer

The equation $x^2 - 16x + 63 = 0$ rewritten by completing the square is $(x - 8)^2 = 1$, which gives the solutions $x = 9$ and $x = 7$.

Key Concept

Completing the Square

Explanation

Completing the square involves creating a perfect square trinomial from a quadratic equation, which allows us to solve for the variable $x$.

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