How to solve 4n^ 2 +2 0n=4200=

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve 4n^ 2 +2 0n=4200= | Equatix

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Question

$$4n^{2}+2\ 0n=4200=$$

Solve for n

$n=5\sqrt{42}\approx 32.403703492$
$n=-5\sqrt{42}\approx -32.403703492$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Multiply $2$ and $0$ to get $0$.

$$4n^{2}+0n=4200$$

Anything times zero gives zero.

$$4n^{2}+0=4200$$

Anything plus zero gives itself.

$$4n^{2}=4200$$

Divide both sides by $4$.

$$n^{2}=\frac{4200}{4}$$

Divide $4200$ by $4$ to get $1050$.

$$n^{2}=1050$$

Take the square root of both sides of the equation.

$$n=5\sqrt{42}$$ $$n=-5\sqrt{42}$$

Steps Using the Quadratic Formula

Multiply $2$ and $0$ to get $0$.

$$4n^{2}+0n=4200$$

Anything times zero gives zero.

$$4n^{2}+0=4200$$

Anything plus zero gives itself.

$$4n^{2}=4200$$

Subtract $4200$ from both sides.

$$4n^{2}-4200=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $4$ for $a$, $0$ for $b$, and $-4200$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$n=\frac{0±\sqrt{0^{2}-4\times 4\left(-4200\right)}}{2\times 4}$$

Square $0$.

$$n=\frac{0±\sqrt{-4\times 4\left(-4200\right)}}{2\times 4}$$

Multiply $-4$ times $4$.

$$n=\frac{0±\sqrt{-16\left(-4200\right)}}{2\times 4}$$

Multiply $-16$ times $-4200$.

$$n=\frac{0±\sqrt{67200}}{2\times 4}$$

Take the square root of $67200$.

$$n=\frac{0±40\sqrt{42}}{2\times 4}$$

Multiply $2$ times $4$.

$$n=\frac{0±40\sqrt{42}}{8}$$

Now solve the equation $n=\frac{0±40\sqrt{42}}{8}$ when $±$ is plus.

$$n=5\sqrt{42}$$

Now solve the equation $n=\frac{0±40\sqrt{42}}{8}$ when $±$ is minus.

$$n=-5\sqrt{42}$$

The equation is now solved.

$$n=5\sqrt{42}$$ $$n=-5\sqrt{42}$$

Show Solution

Basic Math

Pre-Algebra

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Trigonometry

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Precalculus

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Example

Question

Solve for n

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Steps Using the Quadratic Formula