(5/4)x^2 + (1/2)x -22 = 0 ; x=?

Question

(5/4)x^2 + (1/2)x -22 = 0
x[(5/4)x + 1/2] =0
x=?

Answer 1

(5/4)x² + (1/2)x - 22 = 0
and thanks for good use of ().
multiply by 4 to get rid of fractions:
5x² + 2x - 88 = 0
we look for a pair of factors of 5(88) = 440 that differ by 2, which are 20 and 22, so
5x² - 20x + 22x - 88 = 0
5x(x - 4) + 22(x - 4) = 0
(5x + 22)(x - 4) = 0
5x + 22 = 0, x = -22/5
x - 4 = 0, x = 4

Answer 2

multiply thru by 4:

5x^2 + 2x - 88 =0
(5x-22)(x+4) = 0

x = -4, 22/5

Answer 3

(5/4)x^2 +(1/2)x - 22 = 0

multiply with 4

5x^2 + 2x - 88 = 0

5x^2 - 20x + 22x - 88 = 0

5x(x - 4) + 22(x - 4) = 0

(x - 4)(5x + 22) = 0

x = 4 or -22/5

Answer 4

Simplifying
5x^2 + 2x + -88 = 0

Reorder the terms:
-88 + 2x + 5x^2 = 0

Solving
-88 + 2x + 5x^2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-22 + -5x)(4 + -1x) = 0

Subproblem 1
Set the factor '(-22 + -5x)' equal to zero and attempt to solve:

Simplifying
-22 + -5x = 0

Solving
-22 + -5x = 0

Move all terms containing x to the left, all other terms to the right.

Add '22' to each side of the equation.
-22 + 22 + -5x = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -5x = 0 + 22
-5x = 0 + 22

Combine like terms: 0 + 22 = 22
-5x = 22

Divide each side by '-5'.
x = -4.4

Simplifying
x = -4.4
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-4.4, 4}

Answer 5

5x^2 + 2x - 88=0 (orig eq x4)
(5x+22)(x-4)=0
x = 4 or -22/5

Answer 6

Multiply everything by 4 then you have

5x^2 + 2x - 88 = 0

then use quadratic formula