Question

Write the quadratic equation in standard form. Solve using the quadratic formula. $$16=-x^{2}+11 x$$

Short answer

The standard form of the given equation is \(x^2 - 11x + 16 = 0\). The roots of this equation given by the quadratic formula are \(x = (11 + \sqrt{57}) / 2\) and \(x = (11 - \sqrt{57}) / 2\).

Step-by-step solution

Rewrite Equation in Standard Form

Move all terms to one side of the equation to achieve this standard form. Therefore, the equation can be rewritten as \(x^2 - 11x + 16 = 0\).

Identify coefficients

The equation \(x^2 - 11x + 16 = 0\) has coefficients a=1, b=-11, and c=16.

Apply the Quadratic Formula

Substitute the identified coefficients into the quadratic formula to find the roots of the equation. The quadratic formula is \(x = (-b ± \sqrt{b^2 - 4ac}) / (2a)\). Plugging the coefficients into the formula gives \(x = (11 ± \sqrt{(-11)^2 - 4 * 1 * 16}) / (2 * 1)\). This simplifies to \(x = (11 ± \sqrt{121 - 64}) / 2 = (11 ± \sqrt{57}) / 2\). So the roots of the equation are \(x = (11 + \sqrt{57}) / 2\) and \(x = (11 - \sqrt{57}) / 2\).