Solve M^23269/10-3042

Question

Simplify the expression

\frac{3269}{10} M^{2} - 3042

Evaluate

M^{2} \times \frac{3269}{10} - 3042

Solution

\frac{3269}{10} M^{2} - 3042

Show Solution

\frac{1}{10} (3269 M^{2} - 30420)

Evaluate

M^{2} \times \frac{3269}{10} - 3042

Use the commutative property to reorder the terms

\frac{3269}{10} M^{2} - 3042

Solution

\frac{1}{10} (3269 M^{2} - 30420)

Show Solution

M_{1} = - \frac{78 16345}{3269}, M_{2} = \frac{78 16345}{3269}

Alternative Form

M_{1} \approx - 3.050508, M_{2} \approx 3.050508

Evaluate

M^{2} \times \frac{3269}{10} - 3042

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

M^{2} \times \frac{3269}{10} - 3042 = 0

Use the commutative property to reorder the terms

\frac{3269}{10} M^{2} - 3042 = 0

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

\frac{3269}{10} M^{2} = 0 + 3042

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

\frac{3269}{10} M^{2} = 3042

Multiply by the reciprocal

\frac{3269}{10} M^{2} \times \frac{10}{3269} = 3042 \times \frac{10}{3269}

Multiply

M^{2} = 3042 \times \frac{10}{3269}

Multiply

More Steps

Evaluate

3042 \times \frac{10}{3269}

Multiply the numbers

\frac{3042 \times 10}{3269}

Multiply the numbers

\frac{30420}{3269}

M^{2} = \frac{30420}{3269}

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

M = \pm \frac{30420}{3269}

Simplify the expression

More Steps

Evaluate

\frac{30420}{3269}

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

\frac{30420}{3269}

Simplify the radical expression

More Steps

Evaluate

30420

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

6084 \times 5

Write the number in exponential form with the base of 78

7 8^{2} \times 5

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

7 8^{2} \times 5

Reduce the index of the radical and exponent with 2

785

\frac{78 5}{3269}

Multiply by the Conjugate

\frac{78 5 \times 3269}{3269 \times 3269}

Multiply the numbers

More Steps

Evaluate

5 \times 3269

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

5 \times 3269

Calculate the product

16345

\frac{78 16345}{3269 \times 3269}

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

\frac{78 16345}{3269}

M = \pm \frac{78 16345}{3269}

Separate the equation into 2 possible cases

M = \frac{78 16345}{3269} M = - \frac{78 16345}{3269}

Solution

M_{1} = - \frac{78 16345}{3269}, M_{2} = \frac{78 16345}{3269}

Alternative Form

M_{1} \approx - 3.050508, M_{2} \approx 3.050508

Show Solution