Complete the square

Question

3x^2+6x-75=0.solve the equation by completing the square

 

X=

X=

Answer 1

As follow-up to the Michael's solution, the value to be added to both sides can be calculated by...

...looking at your original expression, identify the coefficient "B" of the "x" term. Take one-half the "B" value, then square the result and can written as [½(B)]²or [B/2]². This value is added to both sides of the equation. So, with the above...

B=2..................from Ax²+Bx=C ----> x²+2x=25,

                         original equation
(1/2)2=2/2=1...take one-half of "B"
1²=1.................square the value found in the

                          previous step

This is the exact value Michael added to each side of the equation in his solution to get...

    x²+2x+1=25+1

    x²+2x+1=26

(x+1)(x+1)=26

       (x+1)²=26

 

Remainder of the solution is as Michael illustrates.

Answer 2

Deleted answer.

Answer 3

Divide both sides of the equation by 3 so that the coefficient of x² is 1.

 

x² + 2x - 25 = 0

 

 

Add 26 on both sides of the equation.  Doing so will make the left side of the equation a perfect square trinomial.

 

x² + 2x + 1 = 26

 

(x + 1)(x + 1) = 26

 

(x + 1)² = 26

 

 

Square-root both sides of the equation to undo the square.

 

x + 1 = ±√26

 

 

Subtract 1 on both sides of the equation.

 

x = -1 ± √26

 

 

The plus/minus sign indicates that we have two solutions.

 

x = -1 - √26

x = -1 + √26