Question

How do you solve the equation `x^2 + 12x - 7 = 7x - 5`?

can you please explain how to do this, I made it into 0 and tried to factorise but it didn't work : /

Answer 1

`x=-5/2+1/2sqrt(33)~~0.3723` and
`x=-5/2-1/2sqrt(33)~~-5.3723`

Explanation:

Step 1. Bring all terms over to the left hand side.

Add `5` to both sides

`x^2+12x-2=7x`

Subtract `7x` from both sides

`x^2+5x-2=0`

Step 2. Factor, complete the square, or use quadratic equation to solve.

After several attempts, it quickly becomes clear this does not factor with nice, integer terms. Let's try the quadratic equation:

`x=(-5+-sqrt((5)^2-4(1)(-2)))/(2(1))`

`x=(-5+-sqrt(33))/(2)`

`x=-5/2+1/2sqrt(33)~~0.3723` and
`x=-5/2-1/2sqrt(33)~~-5.3723`

Step 3. Graph the equation and look for the roots. In this interactive graph, you can zoom in to the roots.

graph{x^2+5x-2[-8,5,-10,7]}