SOLUTION: The problem reads: Solve. x^2 - 4x = 3. Please show the step by step process to solve this. Thank you.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: The problem reads: Solve. x^2 - 4x = 3. Please show the step by step process to solve this. Thank you.      Log On


   

Question 89113: The problem reads:
Solve. x^2 - 4x = 3.
Please show the step by step process to solve this.
Thank you.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+-+4x+=+3

x%5E2+-+4x+-3=0 Subtract 3 from both sides

Now let's use the quadratic formula to solve for x:


Starting with the general quadratic

ax%5E2%2Bbx%2Bc=0

the general solution using the quadratic equation is:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29

So lets solve x%5E2-4%2Ax-3=0 ( notice a=1, b=-4, and c=-3)

x+=+%28--4+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A-3+%29%29%2F%282%2A1%29 Plug in a=1, b=-4, and c=-3



x+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A-3+%29%29%2F%282%2A1%29 Negate -4 to get 4



x+=+%284+%2B-+sqrt%28+16-4%2A1%2A-3+%29%29%2F%282%2A1%29 Square -4 to get 16



x+=+%284+%2B-+sqrt%28+16%2B12+%29%29%2F%282%2A1%29 Multiply -4%2A-3%2A1 to get 12



x+=+%284+%2B-+sqrt%28+28+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%284+%2B-+2%2Asqrt%287%29%29%2F%282%2A1%29 Simplify the square root



x+=+%284+%2B-+2%2Asqrt%287%29%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%284+%2B+2%2Asqrt%287%29%29%2F2 or x+=+%284+-+2%2Asqrt%287%29%29%2F2


which split up to


x=%2B4%2F2%2B2%2Asqrt%287%29%2F2 or x=%2B4%2F2-2%2Asqrt%287%29%2F2


and simplify to


x=2%2B1%2Asqrt%287%29 or x=2-1%2Asqrt%287%29


Which approximate to

x=4.64575131106459 or x=-0.645751311064591


So our solutions are:
x=4.64575131106459 or x=-0.645751311064591

Notice when we graph x%5E2-4%2Ax-3, we get:



when we use the root finder feature on a calculator, we find that x=4.64575131106459 and x=-0.645751311064591.So this verifies our answer