Seventy five times an integer minus 36 equals the square of the integer? which equation could be used to solve for the unknown integer?

75x - 36 = x²

Step-by-step explanation:

let x be the integer

75x - 36 = x²

More or less, translate each section of the problem in word form into algebraic form.

"Seventy five times an integer" is 75x

"minus 36" is -36

"equals the square of the integer" is = x²

To solve:

Since 75x - 36 = x² is a quadratic, use the quadratic formula.

Rearrange so that all terms are on one side.

This is called standard form (ax² + bx + c = 0)

75x - 36 = x²

0 = x² - 75x + 36

a = 1   b= -75   c=36

 (ignore that weird A)

Substitute a, b and c into the quadratic formula to solve for x, the integer.

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1