Solve M^23269/10-3078

Question

Simplify the expression

\frac{3269}{10} M^{2} - 3078

Evaluate

M^{2} \times \frac{3269}{10} - 3078

Solution

\frac{3269}{10} M^{2} - 3078

Show Solution

\frac{1}{10} (3269 M^{2} - 30780)

Evaluate

M^{2} \times \frac{3269}{10} - 3078

Use the commutative property to reorder the terms

\frac{3269}{10} M^{2} - 3078

Solution

\frac{1}{10} (3269 M^{2} - 30780)

Show Solution

M_{1} = - \frac{18 310555}{3269}, M_{2} = \frac{18 310555}{3269}

Alternative Form

M_{1} \approx - 3.068505, M_{2} \approx 3.068505

Evaluate

M^{2} \times \frac{3269}{10} - 3078

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

M^{2} \times \frac{3269}{10} - 3078 = 0

Use the commutative property to reorder the terms

\frac{3269}{10} M^{2} - 3078 = 0

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

\frac{3269}{10} M^{2} = 0 + 3078

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

\frac{3269}{10} M^{2} = 3078

Multiply by the reciprocal

\frac{3269}{10} M^{2} \times \frac{10}{3269} = 3078 \times \frac{10}{3269}

Multiply

M^{2} = 3078 \times \frac{10}{3269}

Multiply

More Steps

Evaluate

3078 \times \frac{10}{3269}

Multiply the numbers

\frac{3078 \times 10}{3269}

Multiply the numbers

\frac{30780}{3269}

M^{2} = \frac{30780}{3269}

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

M = \pm \frac{30780}{3269}

Simplify the expression

More Steps

Evaluate

\frac{30780}{3269}

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

\frac{30780}{3269}

Simplify the radical expression

More Steps

Evaluate

30780

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

324 \times 95

Write the number in exponential form with the base of 18

1 8^{2} \times 95

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

1 8^{2} \times 95

Reduce the index of the radical and exponent with 2

1895

\frac{18 95}{3269}

Multiply by the Conjugate

\frac{18 95 \times 3269}{3269 \times 3269}

Multiply the numbers

More Steps

Evaluate

95 \times 3269

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

95 \times 3269

Calculate the product

310555

\frac{18 310555}{3269 \times 3269}

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

\frac{18 310555}{3269}

M = \pm \frac{18 310555}{3269}

Separate the equation into 2 possible cases

M = \frac{18 310555}{3269} M = - \frac{18 310555}{3269}

Solution

M_{1} = - \frac{18 310555}{3269}, M_{2} = \frac{18 310555}{3269}

Alternative Form

M_{1} \approx - 3.068505, M_{2} \approx 3.068505

Show Solution