Questions: Solve the equation x^2 - 8x + 7 = 0 by factoring. x =

Solution Steps

To solve the quadratic equation \(x^2 - 8x + 7 = 0\) by factoring, we need to express it in the form \((x - p)(x - q) = 0\), where \(p\) and \(q\) are the roots of the equation. We look for two numbers that multiply to 7 (the constant term) and add up to -8 (the coefficient of the linear term).

The given quadratic equation is: \[ x^2 - 8x + 7 = 0 \]

To factor the quadratic equation, we need to find two numbers that multiply to the constant term, 7, and add up to the coefficient of the linear term, -8. The numbers that satisfy these conditions are -1 and -7.

Using the numbers found in the previous step, we can express the equation in its factored form: \[ (x - 1)(x - 7) = 0 \]

To find the solutions, set each factor equal to zero:

1. \( x - 1 = 0 \) gives \( x = 1 \)
2. \( x - 7 = 0 \) gives \( x = 7 \)

Final Answer