Whats this? #x^2+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- 5sqrt5#

Explanation:

#x^2 + 16x = 61#

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

#x^2 + 16x - 61 = 0# # " 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 + bx + c = 0#

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

#:. 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]}