SOLUTION: COMPLETING THE SQUARE 5-5 Solving a quadratic equation if the coefficient of x^2 is 1 x^2=4x-13

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: COMPLETING THE SQUARE 5-5 Solving a quadratic equation if the coefficient of x^2 is 1 x^2=4x-13      Log On


   

Question 191107: COMPLETING THE SQUARE 5-5
Solving a quadratic equation if the coefficient of x^2 is 1
x^2=4x-13
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


By the numbers:

Step 1: Variables on the left, constants on the right.



Step 2: Divide the coefficient on the 1st order term by 2, square the result, add that result to both sides of the equation (-4 divided by 2 is -2, -2 squared is 4, so add 4 to each side):




Step 3: Now that we have 'completed the square' by creating a perfect square trinomial on the left, factor it:



Step 4: Take the square root:



Clang! Buzz-Buzz-Buzz! Warning, Will Robinson! We have a negative radicand.

Step 5: Factor the -1 out of the radicand:



Step 6: Use the definition of the imaginary number ,namely



Step 7: Add 2 to both sides




John