Solve t^2-200/45 - ScanMath

Question

Simplify the expression

Solution

t^{2} - \frac{40}{9}

Evaluate

t^{2} - \frac{200}{45}

Solution

t^{2} - \frac{40}{9}

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Factor

\frac{1}{9} (9 t^{2} - 40)

Evaluate

t^{2} - \frac{200}{45}

Cancel out the common factor 5

t^{2} - \frac{40}{9}

Solution

\frac{1}{9} (9 t^{2} - 40)

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Find the roots of the algebra expression

t_{1} = - \frac{2 10}{3}, t_{2} = \frac{2 10}{3}

Alternative Form

t_{1} \approx - 2.108185, t_{2} \approx 2.108185

Evaluate

t^{2} - \frac{200}{45}

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

t^{2} - \frac{200}{45} = 0

Cancel out the common factor 5

t^{2} - \frac{40}{9} = 0

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

t^{2} = 0 + \frac{40}{9}

Add the terms

t^{2} = \frac{40}{9}

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

t = \pm \frac{40}{9}

Simplify the expression

More Steps

Evaluate

\frac{40}{9}

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

\frac{40}{9}

Simplify the radical expression

More Steps

Evaluate

40

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

4 \times 10

Write the number in exponential form with the base of 2

2^{2} \times 10

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

2^{2} \times 10

Reduce the index of the radical and exponent with 2

210

\frac{2 10}{9}

Simplify the radical expression

More Steps

Evaluate

9

Write the number in exponential form with the base of 3

3^{2}

Reduce the index of the radical and exponent with 2

3

\frac{2 10}{3}

t = \pm \frac{2 10}{3}

Separate the equation into 2 possible cases

t = \frac{2 10}{3} t = - \frac{2 10}{3}

Solution

t_{1} = - \frac{2 10}{3}, t_{2} = \frac{2 10}{3}

Alternative Form

t_{1} \approx - 2.108185, t_{2} \approx 2.108185

Show Solution