Whats this? x^2+16x=61x2+16x=61

3 Answers
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- 5sqrt5x=8+55,855

Explanation:

x^2 + 16x = 61x2+16x=61

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

x^2 + 16x - 61 = 0x2+16x61=0 " is a quadratic equation which has two values for variable 'x'" is a quadratic equation which has two values for variable 'x'

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

Standard form of quadratic equation is a x^2 + bx + c = 0ax2+bx+c=0

x = (-b +- sqrt(b^2 - 4ac)) / (2a)x=b±b24ac2a

:. a = 1, b = 16, c = -61

x = (-16 +- sqrt(16^2 - 4*1 * -61)) / (2*1)

x = (-16 +- sqrt(256 + 244)) / 2

x = (-16 +- sqrt(500)) / 2 = -8 +- sqrt125

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

Aug 5, 2018

x-intercepts: (-8+5sqrt5,0) and (-8-5sqrt5,0)

Approximate x-intercepts: (3.18,0) and (-19.8,0)

Explanation:

Solve:

x^2+16x=61

Subtract 61 from both sides of the equation.

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

ax^2+bx+c=0,

where:

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

To solve for x, use the quadratic formula.

x=(-b+-sqrt(b^2-4ac))/(2a)

Plug in the known values and solve.

x=(-16+-sqrt(16^2-4*1*-61))/(2*1)

Simplify.

x=(-16+-sqrt(500))/2

Prime factorize 500.

x=(-16+-sqrt(2xx2xx5xx5xx5))/2

x=(-16+-sqrt(2^2xx5^2xx5))/2

Apply rule: sqrt(a^2)=a

x=(-16+-2xx5sqrt5)/2

x=(-16+-10sqrt5)/2

Simplify.

x=-8+-5sqrt5

x=-8+5sqrt5, -8-5sqrt5

x-intercepts: (-8+5sqrt5,0) and (-8-5sqrt5,0)

Approximate x-intercepts: (3.18,0) and (-19.8,0)

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