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Solve for all values of x by factoring X^2+x=0Asked by zeke
Solve for all values of x by factoring.
x2 −9x+8=0
x2 −9x+8=0
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Answered by
GPT-4o mini
To solve the equation \( x^2 - 9x + 8 = 0 \) by factoring, we first need to express the quadratic in the form \( (x - p)(x - q) = 0 \), where \( p \) and \( q \) are the roots we need to find.
We can start by looking for two numbers that multiply to the constant term (8) and add up to the linear coefficient (-9).
The numbers that satisfy this condition are -1 and -8, since:
- \((-1) \times (-8) = 8\)
- \((-1) + (-8) = -9\)
Thus, we can factor the quadratic equation as follows:
\[
x^2 - 9x + 8 = (x - 1)(x - 8)
\]
Setting this equal to zero gives us:
\[
(x - 1)(x - 8) = 0
\]
Now, we can set each factor equal to zero:
1. \( x - 1 = 0 \) → \( x = 1 \)
2. \( x - 8 = 0 \) → \( x = 8 \)
So, the solutions to the equation \( x^2 - 9x + 8 = 0 \) are:
\[
x = 1 \quad \text{and} \quad x = 8
\]
We can start by looking for two numbers that multiply to the constant term (8) and add up to the linear coefficient (-9).
The numbers that satisfy this condition are -1 and -8, since:
- \((-1) \times (-8) = 8\)
- \((-1) + (-8) = -9\)
Thus, we can factor the quadratic equation as follows:
\[
x^2 - 9x + 8 = (x - 1)(x - 8)
\]
Setting this equal to zero gives us:
\[
(x - 1)(x - 8) = 0
\]
Now, we can set each factor equal to zero:
1. \( x - 1 = 0 \) → \( x = 1 \)
2. \( x - 8 = 0 \) → \( x = 8 \)
So, the solutions to the equation \( x^2 - 9x + 8 = 0 \) are:
\[
x = 1 \quad \text{and} \quad x = 8
\]
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