Solve x^2 7x - 288 = 0

Question

x^{2} \times 7 x - 288 = 0

Solve the equation

x = \frac{2 3 1764}{7}

Alternative Form

x \approx 3.452217

Evaluate

x^{2} \times 7 x - 288 = 0

Multiply

More Steps

Evaluate

x^{2} \times 7 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 7

Add the numbers

x^{3} \times 7

Use the commutative property to reorder the terms

7 x^{3}

7 x^{3} - 288 = 0

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

7 x^{3} = 0 + 288

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

7 x^{3} = 288

Divide both sides

\frac{7 x ^{3}}{7} = \frac{288}{7}

Divide the numbers

x^{3} = \frac{288}{7}

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

3 x^{3} = 3 \frac{288}{7}

Calculate

x = 3 \frac{288}{7}

Solution

More Steps

Evaluate

3 \frac{288}{7}

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

\frac{3 288}{3 7}

Simplify the radical expression

More Steps

Evaluate

3288

Write the expression as a product where the root of one of the factors can be evaluated

3 8 \times 36

Write the number in exponential form with the base of 2

3 2^{3} \times 36

The root of a product is equal to the product of the roots of each factor

3 2^{3} \times 336

Reduce the index of the radical and exponent with 3

2336

\frac{2 3 36}{3 7}

Multiply by the Conjugate

\frac{2 3 36 \times 3 7 ^{2}}{3 7 \times 3 7 ^{2}}

Simplify

\frac{2 3 36 \times 3 49}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

336 \times 349

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

3 36 \times 49

Calculate the product

31764

\frac{2 3 1764}{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{2 3 1764}{7}

x = \frac{2 3 1764}{7}

Alternative Form

x \approx 3.452217

Show Solution