Find the Roots (Zeros) 3(x-pi)^2-12

$3 {(x - π)}^{2} - 12$

Step 1

Set $3 {(x - π)}^{2} - 12$ equal to $0$ .

$3 {(x - π)}^{2} - 12 = 0$

Step 2

Solve for $x$ .

Simplify each term.

Rewrite ${(x - π)}^{2}$ as $(x - π) (x - π)$ .

$3 ((x - π) (x - π)) - 12 = 0$

Expand $(x - π) (x - π)$ using the FOIL Method.

Apply the distributive property.

$3 (x (x - π) - π (x - π)) - 12 = 0$

Apply the distributive property.

$3 (x \cdot x + x (- π) - π (x - π)) - 12 = 0$

Apply the distributive property.

$3 (x \cdot x + x (- π) - π x - π (- π)) - 12 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$3 (x^{2} + x (- π) - π x - π (- π)) - 12 = 0$

Multiply $- π (- π)$ .

Multiply $- 1$ by $- 1$ .

$3 (x^{2} + x (- π) - π x + 1 π π) - 12 = 0$

Multiply $π$ by $1$ .

$3 (x^{2} + x (- π) - π x + π π) - 12 = 0$

Raise $π$ to the power of $1$ .

$3 (x^{2} + x (- π) - π x + π^{1} π) - 12 = 0$

Raise $π$ to the power of $1$ .

$3 (x^{2} + x (- π) - π x + π^{1} π^{1}) - 12 = 0$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 (x^{2} + x (- π) - π x + π^{1 + 1}) - 12 = 0$

Add $1$ and $1$ .

$3 (x^{2} + x (- π) - π x + π^{2}) - 12 = 0$

Subtract $π x$ from $x (- π)$ .

Move $x$ .

$3 (x^{2} - π x - π x + π^{2}) - 12 = 0$

Subtract $π x$ from $- π x$ .

$3 (x^{2} - 2 π x + π^{2}) - 12 = 0$

Apply the distributive property.

$3 x^{2} + 3 (- 2 π x) + 3 π^{2} - 12 = 0$

Multiply $- 2$ by $3$ .

$3 x^{2} - 6 π x + 3 π^{2} - 12 = 0$

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx 1.14159265, 5.14159265$

Step 3