Resolved: "Solve by completing the square. 3f2+90f=57 Write your..."

siroticuvj

Answered question

2021-11-16

Solve by completing the square.

3 f^{2} + 90 f = 57

Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.

f = ? or f = ?

Answer & Explanation

Ruth Phillips

Beginner2021-11-17Added 18 answers

Step 1
Given equation $3 f^{2} + 90 f - 57 = 0$
We know that roots of equation $a x^{2} + b x + c = 0 i s \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$
By comparing with the given equation we get:
$a = 3, b = 90 and c = - 57$
Step 2
So the roots are:
$\Rightarrow \frac{- 90 \pm \sqrt{90^{2} - 4 \cdot 3 \cdot - 57}}{2 \cdot 3}$
$\Rightarrow \frac{- 90 \pm \sqrt{8100 + 684}}{6}$
$\Rightarrow \frac{- 90 \pm 12 \sqrt{61}}{6}$
$\Rightarrow - 15 \pm 2 \sqrt{61}$
$\Rightarrow - 15 + 2 \sqrt{61} or - 15 - 2 \sqrt{61}$
$\approx 0.6204 or - 30.6204$
Therefore the roots are 0.620 or -30.620.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Pre-Algebra

Which expression has both 8 and n as factors???
One number is 2 more than 3 times another. Their sum is 22. Find the numbers
8, 14
5, 17
2, 20
4, 18
10, 12
Perform the indicated operation and simplify the result. Leave your answer in factored form
$[\frac{(4 x - 8)}{(- 3 x)}] . [\frac{12}{(12 - 6 x)}]$
An ordered pair set is referred to as a ___?
Please, can u convert 3.16 (6 repeating) to fraction.
Write an algebraic expression for the statement '6 less than the quotient of x divided by 3 equals 2'.
A) $6 - \frac{x}{3} = 2$
B) $\frac{x}{3} - 6 = 2$
C) 3x−6=2
D) $\frac{3}{x} - 6 = 2$
Find: $2.48 \div 4$ .
Multiplication $999 \times 999$ equals.
Solve: (128÷32)÷(−4)=
A) -1
B) 2
C) -4
D) -3
What is $0.78888 ... . .$ converted into a fraction? $(0.7 \bar{8})$
The mixed fraction representation of 7/3 is...
How to write the algebraic expression given: the quotient of 5 plus d and 12 minus w?
Express 200+30+5+4100+71000 as a decimal number and find its hundredths digit.
A)235.47,7
B)235.047,4
C)235.47,4
D)234.057,7
Find four equivalent fractions of the given fraction: $\frac{6}{12}$
How to find the greatest common factor of $80 x^{3}, 30 y x^{2}$ ?