Solve 1.1=1242/400*1242/x

$$1.1= \frac{ 1242 }{ 400 } \times \frac{ 1242 }{ x }$$

Solve for x

$$x = \frac{385641}{110} = 3505\frac{91}{110} \approx 3505.827272727$$

Steps Using Factoring

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 400x, the least common multiple of 400,x.

$$440x=x\times 1242\times \frac{1242}{x}$$

Express x\times \frac{1242}{x} as a single fraction.

$$440x=\frac{x\times 1242}{x}\times 1242$$

Express \frac{x\times 1242}{x}\times 1242 as a single fraction.

$$440x=\frac{x\times 1242\times 1242}{x}$$

Subtract \frac{x\times 1242\times 1242}{x} from both sides.

$$440x-\frac{x\times 1242\times 1242}{x}=0$$

Multiply 1242 and 1242 to get 1542564.

$$440x-\frac{x\times 1542564}{x}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 440x times \frac{x}{x}.

$$\frac{440xx}{x}-\frac{x\times 1542564}{x}=0$$

Since \frac{440xx}{x} and \frac{x\times 1542564}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{440xx-x\times 1542564}{x}=0$$

Do the multiplications in 440xx-x\times 1542564.

$$\frac{440x^{2}-1542564x}{x}=0$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$440x^{2}-1542564x=0$$

Factor out x.

$$x\left(440x-1542564\right)=0$$

To find equation solutions, solve x=0 and 440x-1542564=0.

$$x=0 x=\frac{385641}{110}$$

Variable x cannot be equal to 0.

$$x=\frac{385641}{110}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 400x, the least common multiple of 400,x.

$$440x=x\times 1242\times \frac{1242}{x}$$

Express x\times \frac{1242}{x} as a single fraction.

$$440x=\frac{x\times 1242}{x}\times 1242$$

Express \frac{x\times 1242}{x}\times 1242 as a single fraction.

$$440x=\frac{x\times 1242\times 1242}{x}$$

Subtract \frac{x\times 1242\times 1242}{x} from both sides.

$$440x-\frac{x\times 1242\times 1242}{x}=0$$

Multiply 1242 and 1242 to get 1542564.

$$440x-\frac{x\times 1542564}{x}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 440x times \frac{x}{x}.

$$\frac{440xx}{x}-\frac{x\times 1542564}{x}=0$$

Since \frac{440xx}{x} and \frac{x\times 1542564}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{440xx-x\times 1542564}{x}=0$$

Do the multiplications in 440xx-x\times 1542564.

$$\frac{440x^{2}-1542564x}{x}=0$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$440x^{2}-1542564x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 440 for a, -1542564 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-1542564\right)±\sqrt{\left(-1542564\right)^{2}}}{2\times 440}$$

Take the square root of \left(-1542564\right)^{2}.

$$x=\frac{-\left(-1542564\right)±1542564}{2\times 440}$$

The opposite of -1542564 is 1542564.

$$x=\frac{1542564±1542564}{2\times 440}$$

Multiply 2 times 440.

$$x=\frac{1542564±1542564}{880}$$

Now solve the equation x=\frac{1542564±1542564}{880} when ± is plus. Add 1542564 to 1542564.

$$x=\frac{3085128}{880}$$

Reduce the fraction \frac{3085128}{880} to lowest terms by extracting and canceling out 8.

$$x=\frac{385641}{110}$$

Now solve the equation x=\frac{1542564±1542564}{880} when ± is minus. Subtract 1542564 from 1542564.

$$x=\frac{0}{880}$$

Divide 0 by 880.

$$x=0$$

The equation is now solved.

$$x=\frac{385641}{110} x=0$$

Variable x cannot be equal to 0.

$$x=\frac{385641}{110}$$

Steps for Completing the Square

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 400x, the least common multiple of 400,x.

$$440x=x\times 1242\times \frac{1242}{x}$$

Express x\times \frac{1242}{x} as a single fraction.

$$440x=\frac{x\times 1242}{x}\times 1242$$

Express \frac{x\times 1242}{x}\times 1242 as a single fraction.

$$440x=\frac{x\times 1242\times 1242}{x}$$

Subtract \frac{x\times 1242\times 1242}{x} from both sides.

$$440x-\frac{x\times 1242\times 1242}{x}=0$$

Multiply 1242 and 1242 to get 1542564.

$$440x-\frac{x\times 1542564}{x}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 440x times \frac{x}{x}.

$$\frac{440xx}{x}-\frac{x\times 1542564}{x}=0$$

Since \frac{440xx}{x} and \frac{x\times 1542564}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{440xx-x\times 1542564}{x}=0$$

Do the multiplications in 440xx-x\times 1542564.

$$\frac{440x^{2}-1542564x}{x}=0$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$440x^{2}-1542564x=0$$

Divide both sides by 440.

$$\frac{440x^{2}-1542564x}{440}=\frac{0}{440}$$

Dividing by 440 undoes the multiplication by 440.

$$x^{2}+\left(-\frac{1542564}{440}\right)x=\frac{0}{440}$$

Reduce the fraction \frac{-1542564}{440} to lowest terms by extracting and canceling out 4.

$$x^{2}-\frac{385641}{110}x=\frac{0}{440}$$

Divide 0 by 440.

$$x^{2}-\frac{385641}{110}x=0$$

Divide -\frac{385641}{110}, the coefficient of the x term, by 2 to get -\frac{385641}{220}. Then add the square of -\frac{385641}{220} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{385641}{110}x+\left(-\frac{385641}{220}\right)^{2}=\left(-\frac{385641}{220}\right)^{2}$$

Square -\frac{385641}{220} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{385641}{110}x+\frac{148718980881}{48400}=\frac{148718980881}{48400}$$

Factor x^{2}-\frac{385641}{110}x+\frac{148718980881}{48400}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{385641}{220}\right)^{2}=\frac{148718980881}{48400}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{385641}{220}\right)^{2}}=\sqrt{\frac{148718980881}{48400}}$$

Simplify.

$$x-\frac{385641}{220}=\frac{385641}{220} x-\frac{385641}{220}=-\frac{385641}{220}$$

Add \frac{385641}{220} to both sides of the equation.

$$x=\frac{385641}{110} x=0$$

Variable x cannot be equal to 0.

$$x=\frac{385641}{110}$$