Solve M^23269/10-2016

Question

Simplify the expression

\frac{3269}{10} M^{2} - 2016

Evaluate

M^{2} \times \frac{3269}{10} - 2016

Solution

\frac{3269}{10} M^{2} - 2016

Show Solution

\frac{7}{10} (467 M^{2} - 2880)

Evaluate

M^{2} \times \frac{3269}{10} - 2016

Use the commutative property to reorder the terms

\frac{3269}{10} M^{2} - 2016

Solution

\frac{7}{10} (467 M^{2} - 2880)

Show Solution

M_{1} = - \frac{24 2335}{467}, M_{2} = \frac{24 2335}{467}

Alternative Form

M_{1} \approx - 2.483349, M_{2} \approx 2.483349

Evaluate

M^{2} \times \frac{3269}{10} - 2016

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

M^{2} \times \frac{3269}{10} - 2016 = 0

Use the commutative property to reorder the terms

\frac{3269}{10} M^{2} - 2016 = 0

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

\frac{3269}{10} M^{2} = 0 + 2016

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

\frac{3269}{10} M^{2} = 2016

Multiply by the reciprocal

\frac{3269}{10} M^{2} \times \frac{10}{3269} = 2016 \times \frac{10}{3269}

Multiply

M^{2} = 2016 \times \frac{10}{3269}

Multiply

More Steps

Evaluate

2016 \times \frac{10}{3269}

Reduce the numbers

288 \times \frac{10}{467}

Multiply the numbers

\frac{288 \times 10}{467}

Multiply the numbers

\frac{2880}{467}

M^{2} = \frac{2880}{467}

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

M = \pm \frac{2880}{467}

Simplify the expression

More Steps

Evaluate

\frac{2880}{467}

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

\frac{2880}{467}

Simplify the radical expression

More Steps

Evaluate

2880

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

576 \times 5

Write the number in exponential form with the base of 24

2 4^{2} \times 5

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

2 4^{2} \times 5

Reduce the index of the radical and exponent with 2

245

\frac{24 5}{467}

Multiply by the Conjugate

\frac{24 5 \times 467}{467 \times 467}

Multiply the numbers

More Steps

Evaluate

5 \times 467

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

5 \times 467

Calculate the product

2335

\frac{24 2335}{467 \times 467}

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

\frac{24 2335}{467}

M = \pm \frac{24 2335}{467}

Separate the equation into 2 possible cases

M = \frac{24 2335}{467} M = - \frac{24 2335}{467}

Solution

M_{1} = - \frac{24 2335}{467}, M_{2} = \frac{24 2335}{467}

Alternative Form

M_{1} \approx - 2.483349, M_{2} \approx 2.483349

Show Solution