Solve e-40s^2 - ScanMath

Question

Find the roots

s_{1} = - \frac{10 e}{20}, s_{2} = \frac{10 e}{20}

Alternative Form

s_{1} \approx - 0.260686, s_{2} \approx 0.260686

Evaluate

e - 40 s^{2}

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

e - 40 s^{2} = 0

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

- 40 s^{2} = 0 - e

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

- 40 s^{2} = - e

Change the signs on both sides of the equation

40 s^{2} = e

Divide both sides

\frac{40 s ^{2}}{40} = \frac{e}{40}

Divide the numbers

s^{2} = \frac{e}{40}

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

s = \pm \frac{e}{40}

Simplify the expression

More Steps

Evaluate

\frac{e}{40}

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

\frac{e}{40}

Simplify the radical expression

More Steps

Evaluate

40

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

4 \times 10

Write the number in exponential form with the base of 2

2^{2} \times 10

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

2^{2} \times 10

Reduce the index of the radical and exponent with 2

210

\frac{e}{2 10}

Multiply by the Conjugate

\frac{e \times 10}{2 10 \times 10}

Multiply the numbers

More Steps

Evaluate

e \times 10

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

e \times 10

Calculate the product

10 e

\frac{10 e}{2 10 \times 10}

Multiply the numbers

More Steps

Evaluate

210 \times 10

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

2 \times 10

Multiply the terms

20

\frac{10 e}{20}

s = \pm \frac{10 e}{20}

Separate the equation into 2 possible cases

s = \frac{10 e}{20} s = - \frac{10 e}{20}

Solution

s_{1} = - \frac{10 e}{20}, s_{2} = \frac{10 e}{20}

Alternative Form

s_{1} \approx - 0.260686, s_{2} \approx 0.260686

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