Solve 150^2t^4 225t^2-1=0

Question

Solve the equation

t_{1} = - \frac{3 12}{30}, t_{2} = \frac{3 12}{30}

Alternative Form

t_{1} \approx - 0.076314, t_{2} \approx 0.076314

Evaluate

15 0^{2} t^{4} \times 225 t^{2} - 1 = 0

Multiply

More Steps

Evaluate

15 0^{2} t^{4} \times 225 t^{2}

Multiply the terms with the same base by adding their exponents

15 0^{2} t^{4 + 2} \times 225

Add the numbers

15 0^{2} t^{6} \times 225

Multiply the numbers

More Steps

Evaluate

15 0^{2} \times 225

Evaluate the power

22500 \times 225

Multiply the numbers

5062500

5062500 t^{6}

5062500 t^{6} - 1 = 0

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

5062500 t^{6} = 0 + 1

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

5062500 t^{6} = 1

Divide both sides

\frac{5062500 t ^{6}}{5062500} = \frac{1}{5062500}

Divide the numbers

t^{6} = \frac{1}{5062500}

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

t = \pm 6 \frac{1}{5062500}

Simplify the expression

More Steps

Evaluate

6 \frac{1}{5062500}

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

\frac{6 1}{6 5062500}

Simplify the radical expression

\frac{1}{6 5062500}

Simplify the radical expression

More Steps

Evaluate

65062500

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

6 15625 \times 324

Write the number in exponential form with the base of 5

6 5^{6} \times 324

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

6 5^{6} \times 6324

Reduce the index of the radical and exponent with 6

56324

Simplify the root

5318

\frac{1}{5 3 18}

Multiply by the Conjugate

\frac{3 1 8 ^{2}}{5 3 18 \times 3 1 8 ^{2}}

Simplify

\frac{3 3 12}{5 3 18 \times 3 1 8 ^{2}}

Multiply the numbers

More Steps

Evaluate

5318 \times 3 1 8^{2}

Multiply the terms

5 \times 18

Multiply the terms

90

\frac{3 3 12}{90}

Cancel out the common factor 3

\frac{3 12}{30}

t = \pm \frac{3 12}{30}

Separate the equation into 2 possible cases

t = \frac{3 12}{30} t = - \frac{3 12}{30}

Solution

t_{1} = - \frac{3 12}{30}, t_{2} = \frac{3 12}{30}

Alternative Form

t_{1} \approx - 0.076314, t_{2} \approx 0.076314

Show Solution