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X^2-12x-6=-65 solve for x

2 Answers

5 votes

Answer:

x = 6 + 4.796i and x = 6 - 4.796i

Explanation:

For this problem, we will simply apply the quadratic formula to find the values of x. The quadratic formula is as follows:

x = [-b +/- sqrt(b^2 - 4ac)] / 2a

Using the formula let's find the values of x.

x^2 - 12x - 6 = -65

x^2 - 12x - 6 + 65 = -65 + 65

x^2 - 12x + 59 = 0

The coefficient of x^2 is a, the coefficient of x is b, and the constant 59 is c.

Hence, for our formula we have the following values:

a = 1

b = -12

c = 59

x = [-b +/- sqrt(b^2 - 4ac)] / 2a

x = [-(-12) +/- sqrt( (-12)^2 - 4(1)(59) ) ] / 2(1)

x = [ 12 +/- sqrt ( 144 - 236 ) ] / 2

x = [ 12 +/- sqrt ( -92 ) ] / 2

x = [ 12 +/- sqrt ( -4 * 23 ) ] / 2

x = [ 12 +/- 2i sqrt(23) ] / 2

x = 6 +/- i sqrt(23)

Hence from the formula, we have two possible values for x, both complex solutions. Note, i is an imaginary number.

x = 6 + i sqrt(23) and x = 6 - i sqrt(23)

x = 6 + 4.796i and x = 6 - 4.796i

Cheers.

User Kreig
by
7.4k points
3 votes

Answer:

x

Explanation:

x

User Chirag Nagpal
by
8.0k points

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