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Answer :
To solve the quadratic equation [tex]\(x^2 - 6x + 9 = 0\)[/tex], we can use the method of factoring or completing the square. Let's solve it step-by-step:
1. Identify the Equation Form:
The given equation is in the standard quadratic form [tex]\(ax^2 + bx + c = 0\)[/tex], where:
- [tex]\(a = 1\)[/tex]
- [tex]\(b = -6\)[/tex]
- [tex]\(c = 9\)[/tex]
2. Factor the Quadratic:
Notice that the expression can be written as a perfect square. The term [tex]\(x^2 - 6x + 9\)[/tex] can be expressed as [tex]\((x - 3)^2\)[/tex].
3. Rewrite the Equation:
The equation [tex]\(x^2 - 6x + 9 = 0\)[/tex] can be rewritten as:
[tex]\((x - 3)^2 = 0\)[/tex]
4. Solve for x:
If [tex]\((x - 3)^2 = 0\)[/tex], then [tex]\(x - 3 = 0\)[/tex]. Solving this gives:
[tex]\[
x = 3
\][/tex]
5. Conclusion:
Therefore, the solution to the equation is [tex]\(x = 3\)[/tex].
So the correct answer is:
A) [tex]\(x = 3\)[/tex]
1. Identify the Equation Form:
The given equation is in the standard quadratic form [tex]\(ax^2 + bx + c = 0\)[/tex], where:
- [tex]\(a = 1\)[/tex]
- [tex]\(b = -6\)[/tex]
- [tex]\(c = 9\)[/tex]
2. Factor the Quadratic:
Notice that the expression can be written as a perfect square. The term [tex]\(x^2 - 6x + 9\)[/tex] can be expressed as [tex]\((x - 3)^2\)[/tex].
3. Rewrite the Equation:
The equation [tex]\(x^2 - 6x + 9 = 0\)[/tex] can be rewritten as:
[tex]\((x - 3)^2 = 0\)[/tex]
4. Solve for x:
If [tex]\((x - 3)^2 = 0\)[/tex], then [tex]\(x - 3 = 0\)[/tex]. Solving this gives:
[tex]\[
x = 3
\][/tex]
5. Conclusion:
Therefore, the solution to the equation is [tex]\(x = 3\)[/tex].
So the correct answer is:
A) [tex]\(x = 3\)[/tex]
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