How to solve completing the square? 2x^2-8x-15=0

2 Answers
Feb 14, 2018

x=±11.5+2

Explanation:

2x28x15=0

Completing square method:

  • Separate variable terms from constant term, rearrange the equation:

2x28x=15

  • Make sure the coefficient of x2 is always 1.
    Divide the equation by 2:

x24x=7.5

  • Add 4 to left, completing square.

x24x+4=11.5

  • Factor the expression on the left

(x2)2=11.5

  • Take the square root

(x2)2=±11.5

x2=±11.5

x=±11.5+2 or x=±232+2

Feb 14, 2018

Answer: 2±11.5

Explanation:

2x28x15=0

As we are completing the square of more than one x2, it is best to move the constant (15) to the other side. It's sign therefore, changes - (15 not -15).

2x28x=15

Now we divide through by two, to obtain a single x2

x24x=7.5

To complete the square, the general steps are to take half the coefficient of x. In this case, the coefficient is 4 therefore half is two. We form brackets, leaving:

(x2)2

But, if we multiplied this out we would end up with x24x+4
We don't want this 'extra' 4, so to complete the square, we must SUBTRACT 4, leaving;

(x2)24=7.5

Now we solve like a standard linear equation;
(x2)2=7.5+4
(x2)2=11.5
x2=±11.5
x=2±11.5

Remember: when you move across the equals sign, you carry out the opposite operation
i.e square, square root
add, subtract
multiply, divide.

Also, when you square root a number you get both a positive AND negative number.

Hope this helps!