Solve b=sqrt{100-a}quadp(2sqrt{-a+100}-sqrt{-a+100})

$$b = \sqrt { 100 - a } \quad p ( 2 \sqrt { - a + 100 } - \sqrt { - a + 100 } )$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{b}{p}+100\text{, }&p\neq 0\\a\in \mathrm{C}\text{, }&b=0\text{ and }p=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine 2\sqrt{-a+100} and -\sqrt{-a+100} to get \sqrt{-a+100}.

$$b=\sqrt{100-a}p\sqrt{-a+100}$$

Swap sides so that all variable terms are on the left hand side.

$$\sqrt{100-a}p\sqrt{-a+100}=b$$

Multiply \sqrt{100-a} and \sqrt{-a+100} to get \left(\sqrt{100-a}\right)^{2}.

$$\left(\sqrt{100-a}\right)^{2}p=b$$

Calculate \sqrt{100-a} to the power of 2 and get 100-a.

$$\left(100-a\right)p=b$$

Use the distributive property to multiply 100-a by p.

$$100p-ap=b$$

Subtract 100p from both sides.

$$-ap=b-100p$$

The equation is in standard form.

$$\left(-p\right)a=b-100p$$

Divide both sides by -p.

$$\frac{\left(-p\right)a}{-p}=\frac{b-100p}{-p}$$

Dividing by -p undoes the multiplication by -p.

$$a=\frac{b-100p}{-p}$$

Divide b-100p by -p.

$$a=-\frac{b}{p}+100$$

Solve for b (complex solution)

$$b=-p\left(a-100\right)$$

Solution Steps

Combine 2\sqrt{-a+100} and -\sqrt{-a+100} to get \sqrt{-a+100}.

$$b=\sqrt{100-a}p\sqrt{-a+100}$$

Multiply \sqrt{100-a} and \sqrt{-a+100} to get \left(\sqrt{100-a}\right)^{2}.

$$b=\left(\sqrt{100-a}\right)^{2}p$$

Calculate \sqrt{100-a} to the power of 2 and get 100-a.

$$b=\left(100-a\right)p$$

Use the distributive property to multiply 100-a by p.

$$b=100p-ap$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{b}{p}+100\text{, }&\left(b\leq 0\text{ and }p<0\right)\text{ or }\left(b\geq 0\text{ and }p>0\right)\\a\leq 100\text{, }&b=0\text{ and }p=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine 2\sqrt{-a+100} and -\sqrt{-a+100} to get \sqrt{-a+100}.

$$b=\sqrt{100-a}p\sqrt{-a+100}$$

Swap sides so that all variable terms are on the left hand side.

$$\sqrt{100-a}p\sqrt{-a+100}=b$$

Multiply \sqrt{100-a} and \sqrt{-a+100} to get \left(\sqrt{100-a}\right)^{2}.

$$\left(\sqrt{100-a}\right)^{2}p=b$$

Calculate \sqrt{100-a} to the power of 2 and get 100-a.

$$\left(100-a\right)p=b$$

Use the distributive property to multiply 100-a by p.

$$100p-ap=b$$

Subtract 100p from both sides.

$$-ap=b-100p$$

The equation is in standard form.

$$\left(-p\right)a=b-100p$$

Divide both sides by -p.

$$\frac{\left(-p\right)a}{-p}=\frac{b-100p}{-p}$$

Dividing by -p undoes the multiplication by -p.

$$a=\frac{b-100p}{-p}$$

Divide b-100p by -p.

$$a=-\frac{b}{p}+100$$

Solve for b

$$b=-p\left(a-100\right)$$

$$a\leq 100$$

Solution Steps

Combine 2\sqrt{-a+100} and -\sqrt{-a+100} to get \sqrt{-a+100}.

$$b=\sqrt{100-a}p\sqrt{-a+100}$$

Multiply \sqrt{100-a} and \sqrt{-a+100} to get \left(\sqrt{100-a}\right)^{2}.

$$b=\left(\sqrt{100-a}\right)^{2}p$$

Calculate \sqrt{100-a} to the power of 2 and get 100-a.

$$b=\left(100-a\right)p$$

Use the distributive property to multiply 100-a by p.

$$b=100p-ap$$