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Sia

Question
Math
Posted 6 months ago

Rewrite the equation by completing the square.
x216x+63=0(x+)2=
\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 x216x+63=0x^2 - 16x + 63 = 0, we first need to find the number that will make x216xx^2 - 16x a perfect square trinomial
step 2
The coefficient of xx is 16-16, so we take half of that number, which is 8-8, and then square it to get 6464
step 3
We add and subtract 6464 inside the equation to maintain equality. The equation becomes x216x+6464+63=0x^2 - 16x + 64 - 64 + 63 = 0
step 4
Grouping the perfect square trinomial together and combining the constants, we have (x8)21=0(x - 8)^2 - 1 = 0
step 5
Adding 11 to both sides to isolate the perfect square, we get (x8)2=1(x - 8)^2 = 1
step 6
Taking the square root of both sides, we find that x8=±1x - 8 = \pm 1
step 7
Solving for xx, we get two solutions: x=8+1x = 8 + 1 and x=81x = 8 - 1
step 8
Therefore, the solutions are x=9x = 9 and x=7x = 7
Answer
The equation x216x+63=0x^2 - 16x + 63 = 0 rewritten by completing the square is (x8)2=1(x - 8)^2 = 1, which gives the solutions x=9x = 9 and x=7x = 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 xx.

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