Question

solve 3x^2+x-7=4x

Answer 1

3 x^2+x-7 = 4 x
Move everything to the left hand side.
Subtract 4 x from both sides:
3 x^2-3 x-7 = 0
Write the quadratic equation in standard form.
Divide both sides by 3:
x^2-x-7/3 = 0
Solve the quadratic equation by completing the square.
Add 7/3 to both sides:
x^2-x = 7/3
Take one half of the coefficient of x and square it, then add it to both sides.
Add 1/4 to both sides:
x^2-x+1/4 = 31/12
Factor the left hand side.
Write the left hand side as a square:
(x-1/2)^2 = 31/12
Eliminate the exponent on the left hand side.
Take the square root of both sides:
x-1/2 = sqrt(31/3)/2 or x-1/2 = -sqrt(31/3)/2
Look at the first equation: Solve for x.
Add 1/2 to both sides:
x = 1/2+sqrt(31/3)/2 or x-1/2 = -sqrt(31/3)/2
Look at the second equation: Solve for x.
Add 1/2 to both sides:
Answer: |
| x = 1/2+sqrt(31/3)/2 or x = 1/2-sqrt(31/3)/2

Answer 2

x = 1/2+sqrt(31/3)/2 or x = 1/2-sqrt(31/3)/2