Solve M^23269/10-3115

Question

Simplify the expression

\frac{3269}{10} M^{2} - 3115

Evaluate

M^{2} \times \frac{3269}{10} - 3115

Solution

\frac{3269}{10} M^{2} - 3115

Show Solution

\frac{7}{10} (467 M^{2} - 4450)

Evaluate

M^{2} \times \frac{3269}{10} - 3115

Use the commutative property to reorder the terms

\frac{3269}{10} M^{2} - 3115

Solution

\frac{7}{10} (467 M^{2} - 4450)

Show Solution

M_{1} = - \frac{5 83126}{467}, M_{2} = \frac{5 83126}{467}

Alternative Form

M_{1} \approx - 3.086893, M_{2} \approx 3.086893

Evaluate

M^{2} \times \frac{3269}{10} - 3115

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

M^{2} \times \frac{3269}{10} - 3115 = 0

Use the commutative property to reorder the terms

\frac{3269}{10} M^{2} - 3115 = 0

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

\frac{3269}{10} M^{2} = 0 + 3115

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

\frac{3269}{10} M^{2} = 3115

Multiply by the reciprocal

\frac{3269}{10} M^{2} \times \frac{10}{3269} = 3115 \times \frac{10}{3269}

Multiply

M^{2} = 3115 \times \frac{10}{3269}

Multiply

More Steps

Evaluate

3115 \times \frac{10}{3269}

Reduce the numbers

445 \times \frac{10}{467}

Multiply the numbers

\frac{445 \times 10}{467}

Multiply the numbers

\frac{4450}{467}

M^{2} = \frac{4450}{467}

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

M = \pm \frac{4450}{467}

Simplify the expression

More Steps

Evaluate

\frac{4450}{467}

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

\frac{4450}{467}

Simplify the radical expression

More Steps

Evaluate

4450

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

25 \times 178

Write the number in exponential form with the base of 5

5^{2} \times 178

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

5^{2} \times 178

Reduce the index of the radical and exponent with 2

5178

\frac{5 178}{467}

Multiply by the Conjugate

\frac{5 178 \times 467}{467 \times 467}

Multiply the numbers

More Steps

Evaluate

178 \times 467

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

178 \times 467

Calculate the product

83126

\frac{5 83126}{467 \times 467}

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

\frac{5 83126}{467}

M = \pm \frac{5 83126}{467}

Separate the equation into 2 possible cases

M = \frac{5 83126}{467} M = - \frac{5 83126}{467}

Solution

M_{1} = - \frac{5 83126}{467}, M_{2} = \frac{5 83126}{467}

Alternative Form

M_{1} \approx - 3.086893, M_{2} \approx 3.086893

Show Solution