Solve f(x)=-(x+2,5)^2-1

$$f ( x ) = - ( x + 2,5 ) ^ { 2 } - 1$$

Solve for f

$$f=-x-5-\frac{29}{4x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2,5\right)^{2}.

$$fx=-\left(x^{2}+5x+6,25\right)-1$$

To find the opposite of x^{2}+5x+6,25, find the opposite of each term.

$$fx=-x^{2}-5x-6,25-1$$

Subtract 1 from -6,25 to get -7,25.

$$fx=-x^{2}-5x-7,25$$

The equation is in standard form.

$$xf=-x^{2}-5x-7,25$$

Divide both sides by x.

$$\frac{xf}{x}=\frac{-x^{2}-5x-7,25}{x}$$

Dividing by x undoes the multiplication by x.

$$f=\frac{-x^{2}-5x-7,25}{x}$$

Divide -x^{2}-5x-7,25 by x.

$$f=-x-5-\frac{29}{4x}$$

Solve for x

$$x=\frac{\sqrt{f^{2}+10f-4}-f-5}{2}$$

$$x=\frac{-\sqrt{f^{2}+10f-4}-f-5}{2}\text{, }f\geq \sqrt{29}-5\text{ or }f\leq -\sqrt{29}-5$$