Solve V = 5.5sqrt(0.6l + P/100) | Equatix - Math Solver

Fractions & Decimals

Ratios & Proportions

Basic Number Theory

Integers & Absolute Values

Factors & Multiples

Prime Factorization

Basic Equations & Inequalities

Coordinate Plane & Graphing

Linear Equations & Inequalities

Quadratic Equations

Polynomials & Factoring

Functions & Graphs

Systems of Equations

Trigonometric Functions

Trigonometric Identities & Equations

Right Triangle Trigonometry

Graphing Trigonometric Functions

Limits & Continuity

Derivatives & Applications

Integrals & Applications

Series & Sequences

Multivariable Calculus

Functions & Graphs

Polynomial & Rational Functions

Exponential & Logarithmic Functions

Sequences & Series

Descriptive Statistics

Normal Distribution

Hypothesis Testing

Regression Analysis

Linear Programming

Sets & Counting

Eigenvalues & Eigenvectors

Linear Transformations

Atomic Structure

Thermochemistry

Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$V=5.5\sqrt{0.6l+\frac{P}{100}}$$

Solve for P

$P=\frac{400V^{2}}{121}-60l$
$V\geq 0$

Steps for Solving Radical Equations

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

$$5.5\sqrt{0.6l+\frac{P}{100}}=V$$

Divide both sides of the equation by $5.5$, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{5.5\sqrt{\frac{1}{100}P+\frac{3l}{5}}}{5.5}=\frac{V}{5.5}$$

Dividing by $5.5$ undoes the multiplication by $5.5$.

$$\sqrt{\frac{1}{100}P+\frac{3l}{5}}=\frac{V}{5.5}$$

Divide $V$ by $5.5$ by multiplying $V$ by the reciprocal of $5.5$.

$$\sqrt{\frac{1}{100}P+\frac{3l}{5}}=\frac{2V}{11}$$

Square both sides of the equation.

$$\frac{1}{100}P+\frac{3l}{5}=\frac{4V^{2}}{121}$$

Subtract $0.6l$ from both sides of the equation.

$$\frac{1}{100}P+\frac{3l}{5}-\frac{3l}{5}=\frac{4V^{2}}{121}-\frac{3l}{5}$$

Subtracting $0.6l$ from itself leaves $0$.

$$\frac{1}{100}P=\frac{4V^{2}}{121}-\frac{3l}{5}$$

Multiply both sides by $100$.

$$\frac{\frac{1}{100}P}{\frac{1}{100}}=\frac{\frac{4V^{2}}{121}-\frac{3l}{5}}{\frac{1}{100}}$$

Dividing by $\frac{1}{100}$ undoes the multiplication by $\frac{1}{100}$.

$$P=\frac{\frac{4V^{2}}{121}-\frac{3l}{5}}{\frac{1}{100}}$$

Divide $\frac{4V^{2}}{121}-\frac{3l}{5}$ by $\frac{1}{100}$ by multiplying $\frac{4V^{2}}{121}-\frac{3l}{5}$ by the reciprocal of $\frac{1}{100}$.

$$P=\frac{400V^{2}}{121}-60l$$

Solve for P (complex solution)

$P=\frac{400V^{2}}{121}-60l$
$arg(V)<\pi \text{ or }V=0$

Solve for V (complex solution)

$V=\frac{11\sqrt{P+60l}}{20}$

Solve for V

$V=\frac{11\sqrt{P+60l}}{20}$
$l\geq -\frac{P}{60}$