What is the general solution for -25=(29cos(x))*3.7-4.9*3.7^2 ?

The general solution for -25=(29cos(x))*3.7-4.9*3.7^2 is x=1.16779…+2pin,x=2pi-1.16779…+2pin

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-25=(29cos(x))3.7-4.93.7^2

- 25 = (29 cos (x)) \cdot 3.7 - 4.9 \cdot 3. 7^{2}

x = 1.16779 \dots + 2 πn, x = 2 π - 1.16779 \dots + 2 πn

Degrees

x = 66.90973 \dots^{\circ} + 36 0^{\circ} n, x = 293.09026 \dots^{\circ} + 36 0^{\circ} n

Solution steps

- 25 = (29 cos (x)) \cdot 3.7 - 4.9 \cdot 3. 7^{2}

Switch sides

29 cos (x) \cdot 3.7 - 4.9 \cdot 3. 7^{2} = - 25

Multiply the numbers:

29 \cdot 3.7 = 107.3

107.3 cos (x) - 3. 7^{2} \cdot 4.9 = - 25

4.9 \cdot 3. 7^{2} = 67.081

4.9 \cdot 3. 7^{2}

3. 7^{2} = 13.69

= 4.9 \cdot 13.69

Multiply the numbers:

4.9 \cdot 13.69 = 67.081

= 67.081

107.3 cos (x) - 67.081 = - 25

Multiply both sides by

1000

107.3 cos (x) - 67.081 = - 25

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

3

digits to the right of the decimal point, therefore multiply by

1000

107.3 cos (x) \cdot 1000 - 67.081 \cdot 1000 = - 25 \cdot 1000

Refine

107300 cos (x) - 67081 = - 25000

107300 cos (x) - 67081 = - 25000

Move

67081

to the right side

107300 cos (x) - 67081 = - 25000

Add

67081

to both sides

107300 cos (x) - 67081 + 67081 = - 25000 + 67081

Simplify

107300 cos (x) = 42081

107300 cos (x) = 42081

Divide both sides by

107300

107300 cos (x) = 42081

Divide both sides by

107300

\frac{107300 cos ( x )}{107300} = \frac{42081}{107300}

Simplify

cos (x) = \frac{42081}{107300}

cos (x) = \frac{42081}{107300}

Apply trig inverse properties

cos (x) = \frac{42081}{107300}

General solutions for

cos (x) = \frac{42081}{107300}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

x = arccos (\frac{42081}{107300}) + 2 πn, x = 2 π - arccos (\frac{42081}{107300}) + 2 πn

x = arccos (\frac{42081}{107300}) + 2 πn, x = 2 π - arccos (\frac{42081}{107300}) + 2 πn

Show solutions in decimal form

x = 1.16779 \dots + 2 πn, x = 2 π - 1.16779 \dots + 2 πn

What is the general solution for -25=(29cos(x))*3.7-4.9*3.7^2 ?
The general solution for -25=(29cos(x))*3.7-4.9*3.7^2 is x=1.16779…+2pin,x=2pi-1.16779…+2pin