Solve e^2100-7s^2

Question

Simplify the expression

100 e^{2} - 7 s^{2}

Evaluate

e^{2} \times 100 - 7 s^{2}

Solution

100 e^{2} - 7 s^{2}

Show Solution

s_{1} = - \frac{10 7 \times e}{7}, s_{2} = \frac{10 7 \times e}{7}

Alternative Form

s_{1} \approx - 10.27414, s_{2} \approx 10.27414

Evaluate

e^{2} \times 100 - 7 s^{2}

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

e^{2} \times 100 - 7 s^{2} = 0

Multiply the numbers

100 e^{2} - 7 s^{2} = 0

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

- 7 s^{2} = 0 - 100 e^{2}

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

- 7 s^{2} = - 100 e^{2}

Change the signs on both sides of the equation

7 s^{2} = 100 e^{2}

Divide both sides

\frac{7 s ^{2}}{7} = \frac{100 e ^{2}}{7}

Divide the numbers

s^{2} = \frac{100 e ^{2}}{7}

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

s = \pm \frac{100 e ^{2}}{7}

Simplify the expression

More Steps

Evaluate

\frac{100 e ^{2}}{7}

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

\frac{100 e ^{2}}{7}

Simplify the radical expression

More Steps

Evaluate

100 e^{2}

Rewrite the expression

100 \times e^{2}

Simplify the root

10 e

\frac{10 e}{7}

Multiply by the Conjugate

\frac{10 e 7}{7 \times 7}

Use the commutative property to reorder the terms

\frac{10 7 \times e}{7 \times 7}

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

\frac{10 7 \times e}{7}

s = \pm \frac{10 7 \times e}{7}

Separate the equation into 2 possible cases

s = \frac{10 7 \times e}{7} s = - \frac{10 7 \times e}{7}

Solution

s_{1} = - \frac{10 7 \times e}{7}, s_{2} = \frac{10 7 \times e}{7}

Alternative Form

s_{1} \approx - 10.27414, s_{2} \approx 10.27414

Show Solution