Solve 225 x ^ 2 - 1040*276

Question

Simplify the expression

225 x^{2} - 287040

Evaluate

225 x^{2} - 1040 \times 276

Solution

225 x^{2} - 287040

Show Solution

15 (15 x^{2} - 19136)

Evaluate

225 x^{2} - 1040 \times 276

Multiply the numbers

225 x^{2} - 287040

Solution

15 (15 x^{2} - 19136)

Show Solution

x_{1} = - \frac{8 4485}{15}, x_{2} = \frac{8 4485}{15}

Alternative Form

x_{1} \approx - 35.717409, x_{2} \approx 35.717409

Evaluate

225 x^{2} - 1040 \times 276

To find the roots of the expression,set the expression equal to 0

225 x^{2} - 1040 \times 276 = 0

Multiply the numbers

225 x^{2} - 287040 = 0

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

225 x^{2} = 0 + 287040

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

225 x^{2} = 287040

Divide both sides

\frac{225 x ^{2}}{225} = \frac{287040}{225}

Divide the numbers

x^{2} = \frac{287040}{225}

Cancel out the common factor 15

x^{2} = \frac{19136}{15}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm \frac{19136}{15}

Simplify the expression

More Steps

Evaluate

\frac{19136}{15}

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

\frac{19136}{15}

Simplify the radical expression

More Steps

Evaluate

19136

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

64 \times 299

Write the number in exponential form with the base of 8

8^{2} \times 299

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

8^{2} \times 299

Reduce the index of the radical and exponent with 2

8299

\frac{8 299}{15}

Multiply by the Conjugate

\frac{8 299 \times 15}{15 \times 15}

Multiply the numbers

More Steps

Evaluate

299 \times 15

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

299 \times 15

Calculate the product

4485

\frac{8 4485}{15 \times 15}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{8 4485}{15}

x = \pm \frac{8 4485}{15}

Separate the equation into 2 possible cases

x = \frac{8 4485}{15} x = - \frac{8 4485}{15}

Solution

x_{1} = - \frac{8 4485}{15}, x_{2} = \frac{8 4485}{15}

Alternative Form

x_{1} \approx - 35.717409, x_{2} \approx 35.717409

Show Solution