Solve t^2 1224 = t^4

Question

Solve the equation

t_{1} = - 634, t_{2} = 0, t_{3} = 634

Alternative Form

t_{1} \approx - 34.985711, t_{2} = 0, t_{3} \approx 34.985711

Evaluate

t^{2} \times 1224 = t^{4}

Use the commutative property to reorder the terms

1224 t^{2} = t^{4}

Move the expression to the left side

1224 t^{2} - t^{4} = 0

Factor the expression

t^{2} (1224 - t^{2}) = 0

Separate the equation into 2 possible cases

t^{2} = 0 1224 - t^{2} = 0

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

t = 0 1224 - t^{2} = 0

Solve the equation

More Steps

Evaluate

1224 - t^{2} = 0

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

- t^{2} = 0 - 1224

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

- t^{2} = - 1224

Change the signs on both sides of the equation

t^{2} = 1224

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

t = \pm 1224

Simplify the expression

More Steps

Evaluate

1224

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

36 \times 34

Write the number in exponential form with the base of 6

6^{2} \times 34

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

6^{2} \times 34

Reduce the index of the radical and exponent with 2

634

t = \pm 634

Separate the equation into 2 possible cases

t = 634 t = - 634

t = 0 t = 634 t = - 634

Solution

t_{1} = - 634, t_{2} = 0, t_{3} = 634

Alternative Form

t_{1} \approx - 34.985711, t_{2} = 0, t_{3} \approx 34.985711

Show Solution