Solve eta^28-24-2

Question

Simplify the expression

8 η^{2} - 26

Evaluate

η^{2} \times 8 - 24 - 2

Use the commutative property to reorder the terms

8 η^{2} - 24 - 2

Solution

8 η^{2} - 26

Show Solution

2 (4 η^{2} - 13)

Evaluate

η^{2} \times 8 - 24 - 2

Use the commutative property to reorder the terms

8 η^{2} - 24 - 2

Subtract the numbers

8 η^{2} - 26

Solution

2 (4 η^{2} - 13)

Show Solution

η_{1} = - \frac{13}{2}, η_{2} = \frac{13}{2}

Alternative Form

η_{1} \approx - 1.802776, η_{2} \approx 1.802776

Evaluate

η^{2} \times 8 - 24 - 2

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

η^{2} \times 8 - 24 - 2 = 0

Use the commutative property to reorder the terms

8 η^{2} - 24 - 2 = 0

Subtract the numbers

8 η^{2} - 26 = 0

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

8 η^{2} = 0 + 26

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

8 η^{2} = 26

Divide both sides

\frac{8 η ^{2}}{8} = \frac{26}{8}

Divide the numbers

η^{2} = \frac{26}{8}

Cancel out the common factor 2

η^{2} = \frac{13}{4}

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

η = \pm \frac{13}{4}

Simplify the expression

More Steps

Evaluate

\frac{13}{4}

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

\frac{13}{4}

Simplify the radical expression

More Steps

Evaluate

4

Write the number in exponential form with the base of 2

2^{2}

Reduce the index of the radical and exponent with 2

2

\frac{13}{2}

η = \pm \frac{13}{2}

Separate the equation into 2 possible cases

η = \frac{13}{2} η = - \frac{13}{2}

Solution

η_{1} = - \frac{13}{2}, η_{2} = \frac{13}{2}

Alternative Form

η_{1} \approx - 1.802776, η_{2} \approx 1.802776

Show Solution