Question

49f² - 140f + 100 = 0​

Answer 1

Answer:

Simplifying

49f2 + -140f + 100 = 0

Reorder the terms:

100 + -140f + 49f2 = 0

Solving

100 + -140f + 49f2 = 0

Solving for variable 'f'.

Factor a trinomial.

(10 + -7f)(10 + -7f) = 0

Subproblem 1

Set the factor '(10 + -7f)' equal to zero and attempt to solve:

Simplifying

10 + -7f = 0

Solving

10 + -7f = 0

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

Add '-10' to each side of the equation.

10 + -10 + -7f = 0 + -10

Combine like terms: 10 + -10 = 0

0 + -7f = 0 + -10

-7f = 0 + -10

Combine like terms: 0 + -10 = -10

-7f = -10

Divide each side by '-7'.

f = 1.428571429

Simplifying

f = 1.428571429

Subproblem 2

Set the factor '(10 + -7f)' equal to zero and attempt to solve:

Simplifying

10 + -7f = 0

Solving

10 + -7f = 0

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

Add '-10' to each side of the equation.

10 + -10 + -7f = 0 + -10

Combine like terms: 10 + -10 = 0

0 + -7f = 0 + -10

-7f = 0 + -10

Combine like terms: 0 + -10 = -10

-7f = -10

Divide each side by '-7'.

f = 1.428571429

Simplifying

f = 1.428571429

Solution

f = {1.428571429, 1.428571429}

Answer 2

Answer:

$(7f - 10)(7f - 10)$

Step-by-step explanation:

$49 {f}^{2} - 140f + 100 = 0 \\ 49 {f}^{2} - 70f - 70f + 100 = 0 \\ 7f(7f - 10) - 10(7f - 10) = 0 \\ (7f - 10)(7f - 10)$