Solving quadratic equations by completing the square explain! 1) r^2 - 4r - 91 = 7 2) x^2 - 10x + 26 = 8 3) k^2 - 4k + 1 = -5 4) b^2 + 2b = -20

1. 2+sqrt(102)

2. 5+sqrt(5)

3. No Solution

4. No Solution

Step-by-step explanation:

1. r^2-4r+4-91=7+4      r^2-2r-2r+4     (r-2)^2-91=11    (r-2)^2=102   r-2=+sqrt(102)

1. x^2-10x+25+26=8+25      x^2-5x-5x+25     (x-5)^2+26=33    (x-5)^2=5          x-5=+sqrt(5)

1. k^2-4k+4+1=-5+4     k^2-2k-2k+4     (k-2)^2+1=-1    (r-2)^2=-2   No Solution

1. b^2+2b+1=-20+1     b^2+b+b+1     (b+1)^2=-19   No Solution

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

86

step-by-step explanation:

find the area of the triangle then multiply by 2 then add the area of the parollelegram multiplied by 2