Question

solve the equation for y.
$y^2 + 63 = 16y$
show your work here

Explanation:

Step1: Rearrange the equation

We start with the equation \( y^{2}+63 = 16y \). To solve for \( y \), we first rearrange it into standard quadratic form \( ax^{2}+bx + c=0 \). Subtract \( 16y \) from both sides:
\( y^{2}-16y + 63=0 \)

Step2: Factor the quadratic

We need to factor \( y^{2}-16y + 63 \). We look for two numbers that multiply to \( 63 \) and add up to \( - 16 \) (the coefficient of \( y \)). The numbers \( -7 \) and \( -9 \) work because \( (-7)\times(-9)=63 \) and \( -7+(-9)=-16 \). So we can factor the quadratic as:
\( (y - 7)(y - 9)=0 \)

Step3: Solve for y

Using the zero - product property, if \( ab = 0 \), then either \( a = 0 \) or \( b = 0 \). So we set each factor equal to zero:

• If \( y - 7=0 \), then \( y=7 \)
• If \( y - 9=0 \), then \( y = 9 \)

Answer:

\( y = 7 \) or \( y=9 \)