Solve sqrt((40t-60)^2 (30t-20)^2)

Question

Simplify the expression

1200 t^{2} - 2600 t + 1200

Evaluate

(40 t - 60)^{2} (30 t - 20)^{2}

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

40000 (2 t - 3)^{2} (3 t - 2)^{2}

Write the number in exponential form with the base of 200

20 0^{2} (2 t - 3)^{2} (3 t - 2)^{2}

Calculate

200 (2 t - 3) (3 t - 2)

Multiply the terms

More Steps

Evaluate

200 (2 t - 3)

Apply the distributive property

200 \times 2 t - 200 \times 3

Multiply the numbers

400 t - 200 \times 3

Multiply the numbers

400 t - 600

(400 t - 600) (3 t - 2)

Apply the distributive property

400 t \times 3 t - 400 t \times 2 - 600 \times 3 t - (- 600 \times 2)

Multiply the terms

More Steps

Evaluate

400 t \times 3 t

Multiply the numbers

1200 t \times t

Multiply the terms

1200 t^{2}

1200 t^{2} - 400 t \times 2 - 600 \times 3 t - (- 600 \times 2)

Multiply the numbers

1200 t^{2} - 800 t - 600 \times 3 t - (- 600 \times 2)

Multiply the numbers

1200 t^{2} - 800 t - 1800 t - (- 600 \times 2)

Multiply the numbers

1200 t^{2} - 800 t - 1800 t - (- 1200)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

1200 t^{2} - 800 t - 1800 t + 1200

Solution

More Steps

Evaluate

- 800 t - 1800 t

Collect like terms by calculating the sum or difference of their coefficients

(- 800 - 1800) t

Subtract the numbers

- 2600 t

1200 t^{2} - 2600 t + 1200

Show Solution

Find the roots

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

Alternative Form

t_{1} = 0. \dot{6}, t_{2} = 1.5

Evaluate

(40 t - 60)^{2} (30 t - 20)^{2}

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

(40 t - 60)^{2} (30 t - 20)^{2} = 0

Since the left-hand side is always positive or 0,and the right-hand side is always 0,the statement is true for any value of t

(40 t - 60)^{2} (30 t - 20)^{2} = 0, t \in R

Calculate

(40 t - 60)^{2} (30 t - 20)^{2} = 0

Simplify the root

More Steps

Evaluate

(40 t - 60)^{2} (30 t - 20)^{2}

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

40000 (2 t - 3)^{2} (3 t - 2)^{2}

Write the number in exponential form with the base of 200

20 0^{2} (2 t - 3)^{2} (3 t - 2)^{2}

Calculate

200 ∣ (2 t - 3) (3 t - 2) ∣

200 ∣ (2 t - 3) (3 t - 2) ∣ = 0

Rewrite the expression

∣ (2 t - 3) (3 t - 2) ∣ = 0

Rewrite the expression

(2 t - 3) (3 t - 2) = 0

Separate the equation into 2 possible cases

2 t - 3 = 0 3 t - 2 = 0

Solve the equation

More Steps

Evaluate

2 t - 3 = 0

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

2 t = 0 + 3

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

2 t = 3

Divide both sides

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

Divide the numbers

t = \frac{3}{2}

t = \frac{3}{2} 3 t - 2 = 0

Solve the equation

More Steps

Evaluate

3 t - 2 = 0

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

3 t = 0 + 2

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

3 t = 2

Divide both sides

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

Divide the numbers

t = \frac{2}{3}

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

Solution

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

Alternative Form

t_{1} = 0. \dot{6}, t_{2} = 1.5

Show Solution