Solve t1 = 1 t^2 = 1/2t1

Question

Solve the system of equations

t = 0

Evaluate

{t \times 1 = 1 \times t^{2} 1 \times t^{2} = \frac{1}{2} t \times 1

Calculate

{t = t^{2} 1 \times t^{2} = \frac{1}{2} t \times 1

Calculate

More Steps

Evaluate

t = t^{2}

Move the expression to the left side

t - t^{2} = 0

Factor the expression

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Evaluate

t - t^{2}

Rewrite the expression

t - t \times t

Factor out t from the expression

t (1 - t)

t (1 - t) = 0

When the product of factors equals 0,at least one factor is 0

t = 0 1 - t = 0

Solve the equation for t

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Evaluate

1 - t = 0

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

- t = 0 - 1

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

- t = - 1

Change the signs on both sides of the equation

t = 1

t = 0 t = 1

Calculate

t = 0 \cup t = 1

{t = 0 \cup t = 1 1 \times t^{2} = \frac{1}{2} t \times 1

Calculate

{t = 0 \cup t = 1 t^{2} = \frac{1}{2} t

Calculate

More Steps

Evaluate

t^{2} = \frac{1}{2} t

Move the expression to the left side

t^{2} - \frac{1}{2} t = 0

Factor the expression

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Evaluate

t^{2} - \frac{1}{2} t

Rewrite the expression

\frac{1}{2} t \times 2 t - \frac{1}{2} t

Factor out \frac{1}{2} t from the expression

\frac{1}{2} t (2 t - 1)

\frac{1}{2} t (2 t - 1) = 0

When the product of factors equals 0,at least one factor is 0

\frac{1}{2} t = 0 2 t - 1 = 0

Solve the equation for t

t = 0 2 t - 1 = 0

Solve the equation for t

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Evaluate

2 t - 1 = 0

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

2 t = 0 + 1

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

2 t = 1

Divide both sides

\frac{2 t}{2} = \frac{1}{2}

Divide the numbers

t = \frac{1}{2}

t = 0 t = \frac{1}{2}

Calculate

t = 0 \cup t = \frac{1}{2}

{t = 0 \cup t = 1 t = 0 \cup t = \frac{1}{2}

Find the intersection

t = 0

Solution

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Check the solution

{0 \times 1 = 1 \times 0^{2} 1 \times 0^{2} = \frac{1}{2} \times 0 \times 1

Simplify

{0 = 0 0 = 0

Evaluate

true

t = 0

Show Solution