How to solve 1734=4(a)^(2)

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 1734=4(a)^(2) | Equatix

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Question

$$1734=4 { a }^{ 2 }$$

Solve for a

$a = \frac{17 \sqrt{6}}{2} \approx 20.820662814$
$a = -\frac{17 \sqrt{6}}{2} \approx -20.820662814$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Divide both sides by $4$.

$$\frac{1734}{4}=a^{2}$$

Reduce the fraction $\frac{1734}{4}$ to lowest terms by extracting and canceling out $2$.

$$\frac{867}{2}=a^{2}$$

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

$$a^{2}=\frac{867}{2}$$

Take the square root of both sides of the equation.

$$a=\frac{17\sqrt{6}}{2}$$ $$a=-\frac{17\sqrt{6}}{2}$$

Steps Using the Quadratic Formula

Divide both sides by $4$.

$$\frac{1734}{4}=a^{2}$$

Reduce the fraction $\frac{1734}{4}$ to lowest terms by extracting and canceling out $2$.

$$\frac{867}{2}=a^{2}$$

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

$$a^{2}=\frac{867}{2}$$

Subtract $\frac{867}{2}$ from both sides.

$$a^{2}-\frac{867}{2}=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $0$ for $b$, and $-\frac{867}{2}$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$a=\frac{0±\sqrt{0^{2}-4\left(-\frac{867}{2}\right)}}{2}$$

Square $0$.

$$a=\frac{0±\sqrt{-4\left(-\frac{867}{2}\right)}}{2}$$

Multiply $-4$ times $-\frac{867}{2}$.

$$a=\frac{0±\sqrt{1734}}{2}$$

Take the square root of $1734$.

$$a=\frac{0±17\sqrt{6}}{2}$$

Now solve the equation $a=\frac{0±17\sqrt{6}}{2}$ when $±$ is plus.

$$a=\frac{17\sqrt{6}}{2}$$

Now solve the equation $a=\frac{0±17\sqrt{6}}{2}$ when $±$ is minus.

$$a=-\frac{17\sqrt{6}}{2}$$

The equation is now solved.

$$a=\frac{17\sqrt{6}}{2}$$ $$a=-\frac{17\sqrt{6}}{2}$$

Show Solution

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Example

Question

Solve for a

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Steps Using the Quadratic Formula