Solve 7r^2-44r^48

Question

Simplify the expression

7 r^{2} - 352 r^{4}

Evaluate

7 r^{2} - 44 r^{4} \times 8

Solution

7 r^{2} - 352 r^{4}

Show Solution

r^{2} (7 - 352 r^{2})

Evaluate

7 r^{2} - 44 r^{4} \times 8

Multiply the terms

7 r^{2} - 352 r^{4}

Rewrite the expression

r^{2} \times 7 - r^{2} \times 352 r^{2}

Solution

r^{2} (7 - 352 r^{2})

Show Solution

r_{1} = - \frac{154}{88}, r_{2} = 0, r_{3} = \frac{154}{88}

Alternative Form

r_{1} \approx - 0.141019, r_{2} = 0, r_{3} \approx 0.141019

Evaluate

7 r^{2} - 44 r^{4} \times 8

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

7 r^{2} - 44 r^{4} \times 8 = 0

Multiply the terms

7 r^{2} - 352 r^{4} = 0

Factor the expression

r^{2} (7 - 352 r^{2}) = 0

Separate the equation into 2 possible cases

r^{2} = 0 7 - 352 r^{2} = 0

The only way a power can be 0 is when the base equals 0

r = 0 7 - 352 r^{2} = 0

Solve the equation

More Steps

Evaluate

7 - 352 r^{2} = 0

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

- 352 r^{2} = 0 - 7

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

- 352 r^{2} = - 7

Change the signs on both sides of the equation

352 r^{2} = 7

Divide both sides

\frac{352 r ^{2}}{352} = \frac{7}{352}

Divide the numbers

r^{2} = \frac{7}{352}

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

r = \pm \frac{7}{352}

Simplify the expression

More Steps

Evaluate

\frac{7}{352}

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

\frac{7}{352}

Simplify the radical expression

\frac{7}{4 22}

Multiply by the Conjugate

\frac{7 \times 22}{4 22 \times 22}

Multiply the numbers

\frac{154}{4 22 \times 22}

Multiply the numbers

\frac{154}{88}

r = \pm \frac{154}{88}

Separate the equation into 2 possible cases

r = \frac{154}{88} r = - \frac{154}{88}

r = 0 r = \frac{154}{88} r = - \frac{154}{88}

Solution

r_{1} = - \frac{154}{88}, r_{2} = 0, r_{3} = \frac{154}{88}

Alternative Form

r_{1} \approx - 0.141019, r_{2} = 0, r_{3} \approx 0.141019

Show Solution