Solution to Equation

Question

what are the solutions to the equation 3x²+15x=18?

Please and thank you in advance!!!

Answer 1

3x^2 +15x = 18

divide by 3

x^2 +5x = 6

subtract 6 from both sides

x^2 +5x -6 = 0

factor (or if you can't figure out the factors, use the quadratic formula)

(x+6)(x-1) = 0

or x = -5/2 + or - (1/2)sqr(25+24) = -2.5 + or - sqr49/2 = -2.5 + or 3.5 = -6 or 1 are the solutions to the problem

if you found the factors,

set each factor equal to zero and solve for x

x+6=0

x =-6

x-1=0

x = 1

x = 1 and x =-6

check the answers, plug the x values into the original equation

3(1)^2 + 15(1) = 3+ 15 = 18

3(-6)^2 + 15(-6) = 3(36) - 90 = 108-90 = 18

the equation represents graphically an upward opening parabola

where the x intercepts are the solutions to the equation.

3x^ + 15x = 18

3(x^2 + 5x -18) = 0

3(x+6)(x-1) = 0

the x intercepts are 1 and -6

3(x^2 +5 + (5/2)^) - 18 - (5/2)^2 = 0

3(x+5/2)^2 - 18 -25/4 = 0

3(x+ 2.5)^2 - 97/4 = 0 is the equation in vertex form a(x-h)^2 + k where (h,k) is the vertex

3(x+2.5)^2 - 24.25 = 0

the vertex is (-2.5, - 24.25) = the minimum point

sometimes it helps to draw a rough sketch of the graph

the x-intercepts, the zeros, the solutions to the quadratic equation, 1 and -6, are equidistant from the x coordinate of the vertex

-6 to -2.5 is 3.5

1 to -2.5 is 3.5