Question

Solve the equation by factoring, by finding square roots, or by using the quadratic formula. $$y^{2}-7 y+6=-6$$

Short answer

The solutions to the equation are \( y = 3 \) and \( y = 4 \).

Step-by-step solution

Simplification

Rewrite the equation in standard form: \( y^{2} - 7y + 6 + 6 = 0 \), which simplifies to \( y^{2} - 7y + 12 = 0 \)

Factoring

Check if it can be factored. As we see, the equation \( y^{2} - 7y + 12 = 0 \) can be factored into (y - 3)(y - 4) = 0.

Solving the Factored Equations

Solve for \( y \) by setting \( y - 3 = 0 \) and \( y - 4 = 0 \), giving \( y = 3 \) and \( y = 4 \) respectively.