Solve 5{-3[-1+3(-2+4)]-5[-2-(-14+sqrt{2})]}

$$5 \{ - 3 [ - 1 + 3 ( - 2 + 4 ) ] - 5 [ - 2 - ( - 14 + \sqrt { 2 } ) ] \}$$

Evaluate

$$25\left(\sqrt{2}-15\right)\approx -339.644660941$$

Solution Steps

Add -2 and 4 to get 2.

$$5\left(-3\left(-1+3\times 2\right)-5\left(-2-\left(-14+\sqrt{2}\right)\right)\right)$$

Multiply 3 and 2 to get 6.

$$5\left(-3\left(-1+6\right)-5\left(-2-\left(-14+\sqrt{2}\right)\right)\right)$$

Add -1 and 6 to get 5.

$$5\left(-3\times 5-5\left(-2-\left(-14+\sqrt{2}\right)\right)\right)$$

Multiply -3 and 5 to get -15.

$$5\left(-15-5\left(-2-\left(-14+\sqrt{2}\right)\right)\right)$$

To find the opposite of -14+\sqrt{2}, find the opposite of each term.

$$5\left(-15-5\left(-2-\left(-14\right)-\sqrt{2}\right)\right)$$

The opposite of -14 is 14.

$$5\left(-15-5\left(-2+14-\sqrt{2}\right)\right)$$

Add -2 and 14 to get 12.

$$5\left(-15-5\left(12-\sqrt{2}\right)\right)$$

Use the distributive property to multiply -5 by 12-\sqrt{2}.

$$5\left(-15-60+5\sqrt{2}\right)$$

Subtract 60 from -15 to get -75.

$$5\left(-75+5\sqrt{2}\right)$$

Use the distributive property to multiply 5 by -75+5\sqrt{2}.

$$-375+25\sqrt{2}$$