Solve 300 * 100/(100 + x) + 300 * 100/(100 - x) = 640 | 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

$$300\times\frac{100}{100+x}+300\times\frac{100}{100-x}=640$$

Solve for x

$x=-25$
$x=25$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Variable $x$ cannot be equal to any of the values $-100,100$ since division by zero is not defined. Multiply both sides of the equation by $\left(x-100\right)\left(x+100\right)$, the least common multiple of $100+x,100-x$.

$$300\left(x-100\right)\times 100+300\left(-1\right)\left(100+x\right)\times 100=640\left(x-100\right)\left(x+100\right)$$

Multiply $300$ and $100$ to get $30000$.

$$30000\left(x-100\right)+300\left(-1\right)\left(100+x\right)\times 100=640\left(x-100\right)\left(x+100\right)$$

Use the distributive property to multiply $30000$ by $x-100$.

$$30000x-3000000+300\left(-1\right)\left(100+x\right)\times 100=640\left(x-100\right)\left(x+100\right)$$

Multiply $300$ and $-1$ to get $-300$.

$$30000x-3000000-300\left(100+x\right)\times 100=640\left(x-100\right)\left(x+100\right)$$

Multiply $-300$ and $100$ to get $-30000$.

$$30000x-3000000-30000\left(100+x\right)=640\left(x-100\right)\left(x+100\right)$$

Use the distributive property to multiply $-30000$ by $100+x$.

$$30000x-3000000-3000000-30000x=640\left(x-100\right)\left(x+100\right)$$

Subtract $3000000$ from $-3000000$ to get $-6000000$.

$$30000x-6000000-30000x=640\left(x-100\right)\left(x+100\right)$$

Combine $30000x$ and $-30000x$ to get $0$.

$$-6000000=640\left(x-100\right)\left(x+100\right)$$

Use the distributive property to multiply $640$ by $x-100$.

$$-6000000=\left(640x-64000\right)\left(x+100\right)$$

Use the distributive property to multiply $640x-64000$ by $x+100$ and combine like terms.

$$-6000000=640x^{2}-6400000$$

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

$$640x^{2}-6400000=-6000000$$

Add $6400000$ to both sides.

$$640x^{2}=-6000000+6400000$$

Add $-6000000$ and $6400000$ to get $400000$.

$$640x^{2}=400000$$

Divide both sides by $640$.

$$x^{2}=\frac{400000}{640}$$

Divide $400000$ by $640$ to get $625$.

$$x^{2}=625$$

Take the square root of both sides of the equation.

$$x=25$$ $$x=-25$$

Steps Using the Quadratic Formula

Variable $x$ cannot be equal to any of the values $-100,100$ since division by zero is not defined. Multiply both sides of the equation by $\left(x-100\right)\left(x+100\right)$, the least common multiple of $100+x,100-x$.

$$300\left(x-100\right)\times 100+300\left(-1\right)\left(100+x\right)\times 100=640\left(x-100\right)\left(x+100\right)$$

Multiply $300$ and $100$ to get $30000$.

$$30000\left(x-100\right)+300\left(-1\right)\left(100+x\right)\times 100=640\left(x-100\right)\left(x+100\right)$$

Use the distributive property to multiply $30000$ by $x-100$.

$$30000x-3000000+300\left(-1\right)\left(100+x\right)\times 100=640\left(x-100\right)\left(x+100\right)$$

Multiply $300$ and $-1$ to get $-300$.

$$30000x-3000000-300\left(100+x\right)\times 100=640\left(x-100\right)\left(x+100\right)$$

Multiply $-300$ and $100$ to get $-30000$.

$$30000x-3000000-30000\left(100+x\right)=640\left(x-100\right)\left(x+100\right)$$

Use the distributive property to multiply $-30000$ by $100+x$.

$$30000x-3000000-3000000-30000x=640\left(x-100\right)\left(x+100\right)$$

Subtract $3000000$ from $-3000000$ to get $-6000000$.

$$30000x-6000000-30000x=640\left(x-100\right)\left(x+100\right)$$

Combine $30000x$ and $-30000x$ to get $0$.

$$-6000000=640\left(x-100\right)\left(x+100\right)$$

Use the distributive property to multiply $640$ by $x-100$.

$$-6000000=\left(640x-64000\right)\left(x+100\right)$$

Use the distributive property to multiply $640x-64000$ by $x+100$ and combine like terms.

$$-6000000=640x^{2}-6400000$$

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

$$640x^{2}-6400000=-6000000$$

Add $6000000$ to both sides.

$$640x^{2}-6400000+6000000=0$$

Add $-6400000$ and $6000000$ to get $-400000$.

$$640x^{2}-400000=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $640$ for $a$, $0$ for $b$, and $-400000$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\times 640\left(-400000\right)}}{2\times 640}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\times 640\left(-400000\right)}}{2\times 640}$$

Multiply $-4$ times $640$.

$$x=\frac{0±\sqrt{-2560\left(-400000\right)}}{2\times 640}$$

Multiply $-2560$ times $-400000$.

$$x=\frac{0±\sqrt{1024000000}}{2\times 640}$$

Take the square root of $1024000000$.

$$x=\frac{0±32000}{2\times 640}$$

Multiply $2$ times $640$.

$$x=\frac{0±32000}{1280}$$

Now solve the equation $x=\frac{0±32000}{1280}$ when $±$ is plus. Divide $32000$ by $1280$.

$$x=25$$

Now solve the equation $x=\frac{0±32000}{1280}$ when $±$ is minus. Divide $-32000$ by $1280$.

$$x=-25$$

The equation is now solved.

$$x=25$$ $$x=-25$$