What is the general solution for cos(x)=-sqrt(1+576/625) ?

The general solution for cos(x)=-sqrt(1+576/625) is No Solution for x\in\mathbb{R}

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cos(x)=-sqrt(1+576/625)

cos (x) = - 1 + \frac{576}{625}

No Solution for x \in R

Solution steps

cos (x) = - 1 + \frac{576}{625}

Simplify

- 1 + \frac{576}{625} : - \frac{1201}{25}

- 1 + \frac{576}{625}

Join

1 + \frac{576}{625} : \frac{1201}{625}

1 + \frac{576}{625}

Convert element to fraction:

1 = \frac{1 \cdot 625}{625}

= \frac{1 \cdot 625}{625} + \frac{576}{625}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{1 \cdot 625 + 576}{625}

1 \cdot 625 + 576 = 1201

1 \cdot 625 + 576

Multiply the numbers:

1 \cdot 625 = 625

= 625 + 576

Add the numbers:

625 + 576 = 1201

= 1201

= \frac{1201}{625}

= - \frac{1201}{625}

Simplify

\frac{1201}{625} : \frac{1201}{25}

\frac{1201}{625}

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \frac{1201}{625}

625 = 25

625

Factor the number:

625 = 2 5^{2}

= 2 5^{2}

Apply radical rule:

2 5^{2} = 25

= 25

= \frac{1201}{25}

= - \frac{1201}{25}

cos (x) = - \frac{1201}{25}

- 1 \leq cos (x) \leq 1

No Solution for x \in R

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What is the general solution for cos(x)=-sqrt(1+576/625) ?
The general solution for cos(x)=-sqrt(1+576/625) is No Solution for x\in\mathbb{R}