Solve 7x^2 90x-900=0

Question

Solve the equation

x = \frac{3 490}{7}

Alternative Form

x \approx 1.126248

Evaluate

7 x^{2} \times 90 x - 900 = 0

Multiply

More Steps

Evaluate

7 x^{2} \times 90 x

Multiply the terms

630 x^{2} \times x

Multiply the terms with the same base by adding their exponents

630 x^{2 + 1}

Add the numbers

630 x^{3}

630 x^{3} - 900 = 0

Move the constant to the right-hand side and change its sign

630 x^{3} = 0 + 900

Removing 0 doesn't change the value,so remove it from the expression

630 x^{3} = 900

Divide both sides

\frac{630 x ^{3}}{630} = \frac{900}{630}

Divide the numbers

x^{3} = \frac{900}{630}

Cancel out the common factor 90

x^{3} = \frac{10}{7}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 \frac{10}{7}

Calculate

x = 3 \frac{10}{7}

Solution

More Steps

Evaluate

3 \frac{10}{7}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{3 10}{3 7}

Multiply by the Conjugate

\frac{3 10 \times 3 7 ^{2}}{3 7 \times 3 7 ^{2}}

Simplify

\frac{3 10 \times 3 49}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

310 \times 349

The product of roots with the same index is equal to the root of the product

3 10 \times 49

Calculate the product

3490

\frac{3 490}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

37 \times 3 7^{2}

The product of roots with the same index is equal to the root of the product

3 7 \times 7^{2}

Calculate the product

3 7^{3}

Reduce the index of the radical and exponent with 3

7

\frac{3 490}{7}

x = \frac{3 490}{7}

Alternative Form

x \approx 1.126248

Show Solution