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Solve.xsquaredminus11xplus30equals0Question content area bottomPart 1Select the correct choice below and fill in any answer boxes within your choice.
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Answered by
GPT-4o mini
To solve the equation \( x^2 - 11x + 30 = 0 \), we can use the factoring method.
1. We need to factor the quadratic equation. We are looking for two numbers that multiply to 30 (the constant term) and add up to -11 (the coefficient of the linear term).
The two numbers that meet these criteria are -5 and -6, since:
\[
-5 \times -6 = 30
\]
\[
-5 + -6 = -11
\]
2. Now, we can write the equation in its factored form:
\[
(x - 5)(x - 6) = 0
\]
3. To find the values of \( x \), we set each factor equal to zero:
\[
x - 5 = 0 \quad \text{or} \quad x - 6 = 0
\]
4. Solving these equations gives:
\[
x = 5 \quad \text{or} \quad x = 6
\]
Thus, the solutions to the equation \( x^2 - 11x + 30 = 0 \) are:
\[
\boxed{5} \quad \text{and} \quad \boxed{6}
\]
1. We need to factor the quadratic equation. We are looking for two numbers that multiply to 30 (the constant term) and add up to -11 (the coefficient of the linear term).
The two numbers that meet these criteria are -5 and -6, since:
\[
-5 \times -6 = 30
\]
\[
-5 + -6 = -11
\]
2. Now, we can write the equation in its factored form:
\[
(x - 5)(x - 6) = 0
\]
3. To find the values of \( x \), we set each factor equal to zero:
\[
x - 5 = 0 \quad \text{or} \quad x - 6 = 0
\]
4. Solving these equations gives:
\[
x = 5 \quad \text{or} \quad x = 6
\]
Thus, the solutions to the equation \( x^2 - 11x + 30 = 0 \) are:
\[
\boxed{5} \quad \text{and} \quad \boxed{6}
\]
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