Question

I have a math final today and i need to know more about solving a quadratic equation by completing the square. A sample problem is
d^2+3d-10=0

Answer 1

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Answer 2

1/2 coefficient of d; square it; add it to both sides

Answer 3

the two roots of a quadratic equation of the the type \[ax^2 +bx +c=0\] are \[-b \pm \sqrt{b^2-4ac}/2a\]

Answer 4

Hi Dimitri, Solution is as follows

Answer 5

first u shift the constant ie -10 to RHS to get
d^2 + 3d = 10

Answer 6

\[-3\pm \sqrt{9--40}/2\] hence the solutions are (-3+7)/2 =2 and (-3-7)/2 =-5

Answer 7

Now add square of half of coefficient of d i.e. (3/2)^2 to both sides to get
d^2 + 3d + (3/2)^2 = 10 + (3/2)^2

Answer 8

LHS becomes equal to (d + 3/2)^2, so we get
(d + 3/2)^2 = 10 + 9/4

Hence (d + 3/2)^2 = 49/4

Answer 9

Further taking root of both sides, we get
d + 3/2 = root(49/4)

so d + 3/2 = +/- 7/2

d = +/- 7/2 - 3/2

Answer 10

So u get two values of d

d = 7/2 - 3/2 = 4/2 = 2

and

d = -7/2 - 3/2 = -10/2 = -5

Answer 11

Is that clear for u Dimitri????