Solve 231 = 2 * 22/7 * x(x + 7) | Equatix - Math Solver

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Example

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

a⋅(b-2)=3b

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

a⋅(b-2)=3b

Question

$$231=2\times\frac{22}{7}\times x(x+7)$$

Solve for x

$x = \frac{7}{2} = 3\frac{1}{2} = 3.5$
$x = -\frac{21}{2} = -10\frac{1}{2} = -10.5$

Steps Using the Quadratic Formula

Steps for Completing the Square

Steps Using the Quadratic Formula

Express $2\times \frac{22}{7}$ as a single fraction.

$$231=\frac{2\times 22}{7}x\left(x+7\right)$$

Multiply $2$ and $22$ to get $44$.

$$231=\frac{44}{7}x\left(x+7\right)$$

Use the distributive property to multiply $\frac{44}{7}x$ by $x+7$.

$$231=\frac{44}{7}xx+\frac{44}{7}x\times 7$$

Multiply $x$ and $x$ to get $x^{2}$.

$$231=\frac{44}{7}x^{2}+\frac{44}{7}x\times 7$$

Cancel out $7$ and $7$.

$$231=\frac{44}{7}x^{2}+44x$$

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

$$\frac{44}{7}x^{2}+44x=231$$

Subtract $231$ from both sides.

$$\frac{44}{7}x^{2}+44x-231=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $\frac{44}{7}$ for $a$, $44$ for $b$, and $-231$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{-44±\sqrt{44^{2}-4\times \frac{44}{7}\left(-231\right)}}{2\times \frac{44}{7}}$$

Square $44$.

$$x=\frac{-44±\sqrt{1936-4\times \frac{44}{7}\left(-231\right)}}{2\times \frac{44}{7}}$$

Multiply $-4$ times $\frac{44}{7}$.

$$x=\frac{-44±\sqrt{1936-\frac{176}{7}\left(-231\right)}}{2\times \frac{44}{7}}$$

Multiply $-\frac{176}{7}$ times $-231$.

$$x=\frac{-44±\sqrt{1936+5808}}{2\times \frac{44}{7}}$$

Add $1936$ to $5808$.

$$x=\frac{-44±\sqrt{7744}}{2\times \frac{44}{7}}$$

Take the square root of $7744$.

$$x=\frac{-44±88}{2\times \frac{44}{7}}$$

Multiply $2$ times $\frac{44}{7}$.

$$x=\frac{-44±88}{\frac{88}{7}}$$

Now solve the equation $x=\frac{-44±88}{\frac{88}{7}}$ when $±$ is plus. Add $-44$ to $88$.

$$x=\frac{44}{\frac{88}{7}}$$

Divide $44$ by $\frac{88}{7}$ by multiplying $44$ by the reciprocal of $\frac{88}{7}$.

$$x=\frac{7}{2}$$

Now solve the equation $x=\frac{-44±88}{\frac{88}{7}}$ when $±$ is minus. Subtract $88$ from $-44$.

$$x=-\frac{132}{\frac{88}{7}}$$

Divide $-132$ by $\frac{88}{7}$ by multiplying $-132$ by the reciprocal of $\frac{88}{7}$.

$$x=-\frac{21}{2}$$

The equation is now solved.

$$x=\frac{7}{2}$$ $$x=-\frac{21}{2}$$

Steps for Completing the Square

Express $2\times \frac{22}{7}$ as a single fraction.

$$231=\frac{2\times 22}{7}x\left(x+7\right)$$

Multiply $2$ and $22$ to get $44$.

$$231=\frac{44}{7}x\left(x+7\right)$$

Use the distributive property to multiply $\frac{44}{7}x$ by $x+7$.

$$231=\frac{44}{7}xx+\frac{44}{7}x\times 7$$

Multiply $x$ and $x$ to get $x^{2}$.

$$231=\frac{44}{7}x^{2}+\frac{44}{7}x\times 7$$

Cancel out $7$ and $7$.

$$231=\frac{44}{7}x^{2}+44x$$

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

$$\frac{44}{7}x^{2}+44x=231$$

Divide both sides of the equation by $\frac{44}{7}$, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{44}{7}x^{2}+44x}{\frac{44}{7}}=\frac{231}{\frac{44}{7}}$$

Dividing by $\frac{44}{7}$ undoes the multiplication by $\frac{44}{7}$.

$$x^{2}+\frac{44}{\frac{44}{7}}x=\frac{231}{\frac{44}{7}}$$

Divide $44$ by $\frac{44}{7}$ by multiplying $44$ by the reciprocal of $\frac{44}{7}$.

$$x^{2}+7x=\frac{231}{\frac{44}{7}}$$

Divide $231$ by $\frac{44}{7}$ by multiplying $231$ by the reciprocal of $\frac{44}{7}$.

$$x^{2}+7x=\frac{147}{4}$$

Divide $7$, the coefficient of the $x$ term, by $2$ to get $\frac{7}{2}$. Then add the square of $\frac{7}{2}$ to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+7x+\left(\frac{7}{2}\right)^{2}=\frac{147}{4}+\left(\frac{7}{2}\right)^{2}$$

Square $\frac{7}{2}$ by squaring both the numerator and the denominator of the fraction.

$$x^{2}+7x+\frac{49}{4}=\frac{147+49}{4}$$

Add $\frac{147}{4}$ to $\frac{49}{4}$ by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+7x+\frac{49}{4}=49$$

Factor $x^{2}+7x+\frac{49}{4}$. In general, when $x^{2}+bx+c$ is a perfect square, it can always be factored as $\left(x+\frac{b}{2}\right)^{2}$.

$$\left(x+\frac{7}{2}\right)^{2}=49$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{7}{2}\right)^{2}}=\sqrt{49}$$

Simplify.

$$x+\frac{7}{2}=7$$ $$x+\frac{7}{2}=-7$$

Subtract $\frac{7}{2}$ from both sides of the equation.

$$x=\frac{7}{2}$$ $$x=-\frac{21}{2}$$