Solve s^2307-41070

Question

Simplify the expression

307 s^{2} - 41070

Evaluate

s^{2} \times 307 - 41070

Solution

307 s^{2} - 41070

Show Solution

s_{1} = - \frac{37 9210}{307}, s_{2} = \frac{37 9210}{307}

Alternative Form

s_{1} \approx - 11.566266, s_{2} \approx 11.566266

Evaluate

s^{2} \times 307 - 41070

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

s^{2} \times 307 - 41070 = 0

Use the commutative property to reorder the terms

307 s^{2} - 41070 = 0

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

307 s^{2} = 0 + 41070

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

307 s^{2} = 41070

Divide both sides

\frac{307 s ^{2}}{307} = \frac{41070}{307}

Divide the numbers

s^{2} = \frac{41070}{307}

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

s = \pm \frac{41070}{307}

Simplify the expression

More Steps

Evaluate

\frac{41070}{307}

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

\frac{41070}{307}

Simplify the radical expression

More Steps

Evaluate

41070

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

1369 \times 30

Write the number in exponential form with the base of 37

3 7^{2} \times 30

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

3 7^{2} \times 30

Reduce the index of the radical and exponent with 2

3730

\frac{37 30}{307}

Multiply by the Conjugate

\frac{37 30 \times 307}{307 \times 307}

Multiply the numbers

More Steps

Evaluate

30 \times 307

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

30 \times 307

Calculate the product

9210

\frac{37 9210}{307 \times 307}

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

\frac{37 9210}{307}

s = \pm \frac{37 9210}{307}

Separate the equation into 2 possible cases

s = \frac{37 9210}{307} s = - \frac{37 9210}{307}

Solution

s_{1} = - \frac{37 9210}{307}, s_{2} = \frac{37 9210}{307}

Alternative Form

s_{1} \approx - 11.566266, s_{2} \approx 11.566266

Show Solution