Which are the solutions of the quadratic equation? x2 = 9x + 6 startfraction negative 9 minus startroot 105 endroot over 2 endfraction comma startfraction negative 9 + startroot 105 endroot over 2 endfraction startfraction negative 9 minus startroot 57 endroot over 2 endfraction comma startfraction negative 9 + startroot 57 endroot over 2 endfraction startfraction 9 minus startroot 105 endroot over 2 endfraction comma startfraction 9 + startroot 105 endroot over 2 endfraction startfraction 9 minus startroot 57 endroot over 2 endfraction comma startfraction 9 + startroot 57 endroot over 2 endfraction

The correct answer is C. 9 -√ 105/ 2,  9 + √ 105/ 2

Step-by-step explanation:

Let's find the solutions for the quadratic equation:

x² = 9x + 6

x² - 9x -6 = 0

Using the quadratic formula, we have:

x = [- (-9) +/- √ (-9)² - 4 * 1 * -6]/2 * 1

x = [ 9 +/- √ (81 + 24]/2

x = [ 9 +/- √ (105]/2

x₁  =  [ 9 + √ (105]/2

x₂ =  [ 9 - √ (105]/2

The correct answer is C. 9 -√ 105/ 2,  9 + √ 105/ 2

Note: Same answer than question 14133688, answered by me today.

x = 9+√105/2 or 9-√105/2

Step-by-step explanation:

Given the quadratic function x² = 9x+6

Re arranging we have;

x²-9x-6 = 0

Comparing this equation to general form ax²+bx+c = 0;

a = 1, b = -9, c = -6

Using the general formula to find x.

x = -b±√b²-4ac/2a

x = -(-9)±√81-4(1)(-6)/2

x = 9±√81+24/2

x = 9±√105/2

x = 9+√105/2 or 9-√105/2

step-by-step explanation:

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form