Solve Using the Quadratic Formula 10/m+1=4m

$\frac{10}{m} + 1 = 4 m$

Subtract $4 m$ from both sides of the equation.

$\frac{10}{m} + 1 - 4 m = 0$

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$m, 1, 1, 1$

The LCM of one and any expression is the expression.

$m$

Multiply each term in $\frac{10}{m} + 1 - 4 m = 0$ by $m$ to eliminate the fractions.

Multiply each term in $\frac{10}{m} + 1 - 4 m = 0$ by $m$ .

$\frac{10}{m} m + 1 m - 4 m \cdot m = 0 m$

Simplify the left side.

Simplify each term.

Cancel the common factor of $m$ .

Cancel the common factor.

$\frac{10}{m} m + 1 m - 4 m \cdot m = 0 m$

Rewrite the expression.

$10 + 1 m - 4 m \cdot m = 0 m$

Multiply $m$ by $1$ .

$10 + m - 4 m \cdot m = 0 m$

Multiply $m$ by $m$ by adding the exponents.

Move $m$ .

$10 + m - 4 (m \cdot m) = 0 m$

Multiply $m$ by $m$ .

$10 + m - 4 m^{2} = 0 m$

Simplify the right side.

Multiply $0$ by $m$ .

$10 + m - 4 m^{2} = 0$

Solve the equation.

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Substitute the values $a = - 4$ , $b = 1$ , and $c = 10$ into the quadratic formula and solve for $m$ .

$\frac{- 1 \pm \sqrt{1^{2} - 4 \cdot (- 4 \cdot 10)}}{2 \cdot - 4}$

Simplify.

Simplify the numerator.

One to any power is one.

$m = \frac{- 1 \pm \sqrt{1 - 4 \cdot - 4 \cdot 10}}{2 \cdot - 4}$

Multiply $- 4$ by $- 4$ .

$m = \frac{- 1 \pm \sqrt{1 + 16 \cdot 10}}{2 \cdot - 4}$

Multiply $16$ by $10$ .

$m = \frac{- 1 \pm \sqrt{1 + 160}}{2 \cdot - 4}$

Add $1$ and $160$ .

$m = \frac{- 1 \pm \sqrt{161}}{2 \cdot - 4}$

Multiply $2$ by $- 4$ .

$m = \frac{- 1 \pm \sqrt{161}}{- 8}$

Simplify $\frac{- 1 \pm \sqrt{161}}{- 8}$ .

$m = \frac{1 \pm \sqrt{161}}{8}$

The final answer is the combination of both solutions.

$m = \frac{1 + \sqrt{161}}{8}, \frac{1 - \sqrt{161}}{8}$

$m = \frac{1 \pm \sqrt{161}}{8}$

The result can be shown in multiple forms.

Exact Form:

$m = \frac{1 \pm \sqrt{161}}{8}$

Decimal Form:

$m = 1.71107219 \dots, - 1.46107219 \dots$

Solve Using the Quadratic Formula 10/m+1=4m

Related Questions

Support LCMGCF.com by disabling your adblocker.