# Whats this? x^2+16x=61

Aug 5, 2018

This is a trinomial

#### Explanation:

This trinomial can be solved using the quadratic equation.

Aug 5, 2018

color(maroon)(x = -8 + 5sqrt5, -8- 5sqrt5

#### Explanation:

${x}^{2} + 16 x = 61$

A trinomial is a 3 term polynomial. For example, 5x2 − 2x + 3 is a trinomial.

${x}^{2} + 16 x - 61 = 0$ $\text{ is a quadratic equation which has two values for variable 'x'}$

"Degree of equation " color(crimson)(2), " no. of terms " color(crimson)(3, " trinomial")

Standard form of quadratic equation is $a {x}^{2} + b x + c = 0$

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

$\therefore a = 1 , b = 16 , c = - 61$

$x = \frac{- 16 \pm \sqrt{{16}^{2} - 4 \cdot 1 \cdot - 61}}{2 \cdot 1}$

$x = \frac{- 16 \pm \sqrt{256 + 244}}{2}$

$x = \frac{- 16 \pm \sqrt{500}}{2} = - 8 \pm \sqrt{125}$

color(maroon)(x = -8 + 5sqrt5, -8- 5sqrt5

Aug 5, 2018

x-intercepts: $\left(- 8 + 5 \sqrt{5} , 0\right)$ and $\left(- 8 - 5 \sqrt{5} , 0\right)$

Approximate x-intercepts: $\left(3.18 , 0\right)$ and $\left(- 19.8 , 0\right)$

#### Explanation:

Solve:

${x}^{2} + 16 x = 61$

Subtract $61$ from both sides of the equation.

${x}^{2} + 16 x - 61 = 0$ is a quadratic equation in standard form, set equal to $0$ rather than $y$ so we can solve for the x-intercepts:

$a {x}^{2} + b x + c = 0$,

where:

$a = 1$, $b = 16$, and c="-61

To solve for $x$, use the quadratic formula.

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

Plug in the known values and solve.

$x = \frac{- 16 \pm \sqrt{{16}^{2} - 4 \cdot 1 \cdot - 61}}{2 \cdot 1}$

Simplify.

$x = \frac{- 16 \pm \sqrt{500}}{2}$

Prime factorize $500$.

$x = \frac{- 16 \pm \sqrt{2 \times 2 \times 5 \times 5 \times 5}}{2}$

$x = \frac{- 16 \pm \sqrt{{2}^{2} \times {5}^{2} \times 5}}{2}$

Apply rule: $\sqrt{{a}^{2}} = a$

$x = \frac{- 16 \pm 2 \times 5 \sqrt{5}}{2}$

$x = \frac{- 16 \pm 10 \sqrt{5}}{2}$

Simplify.

$x = - 8 \pm 5 \sqrt{5}$

$x = - 8 + 5 \sqrt{5} , - 8 - 5 \sqrt{5}$

x-intercepts: $\left(- 8 + 5 \sqrt{5} , 0\right)$ and $\left(- 8 - 5 \sqrt{5} , 0\right)$

Approximate x-intercepts: $\left(3.18 , 0\right)$ and $\left(- 19.8 , 0\right)$

graph{y=x^2+16x-61 [-14.02, 8.48, -7.83, 3.42]}