Solve {left(-(-5w)/1right)}^2-18-7{left(-1/1right)}^24=0

$${ \left( \frac{ -(-5w) }{ 1 } \right) }^{ 2 } -18-7 { \left( \frac{ -1 }{ 1 } \right) }^{ 24 } = 0$$

Solve for w

$$w=1$$

$$w=-1$$

Steps Using Difference of Squares

The opposite of -5w is 5w.

$$\left(\frac{5w}{1}\right)^{2}-18-7\times \left(\frac{-1}{1}\right)^{24}=0$$

Anything divided by one gives itself.

$$\left(5w\right)^{2}-18-7\times \left(\frac{-1}{1}\right)^{24}=0$$

Expand \left(5w\right)^{2}.

$$5^{2}w^{2}-18-7\times \left(\frac{-1}{1}\right)^{24}=0$$

Calculate 5 to the power of 2 and get 25.

$$25w^{2}-18-7\times \left(\frac{-1}{1}\right)^{24}=0$$

Anything divided by one gives itself.

$$25w^{2}-18-7\left(-1\right)^{24}=0$$

Calculate -1 to the power of 24 and get 1.

$$25w^{2}-18-7\times 1=0$$

Multiply 7 and 1 to get 7.

$$25w^{2}-18-7=0$$

Subtract 7 from -18 to get -25.

$$25w^{2}-25=0$$

Divide both sides by 25.

$$w^{2}-1=0$$

Consider w^{2}-1. Rewrite w^{2}-1 as w^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(w-1\right)\left(w+1\right)=0$$

To find equation solutions, solve w-1=0 and w+1=0.

$$w=1 w=-1$$

Steps by Finding Square Root

The opposite of -5w is 5w.

$$\left(\frac{5w}{1}\right)^{2}-18-7\times \left(\frac{-1}{1}\right)^{24}=0$$

Anything divided by one gives itself.

$$\left(5w\right)^{2}-18-7\times \left(\frac{-1}{1}\right)^{24}=0$$

Expand \left(5w\right)^{2}.

$$5^{2}w^{2}-18-7\times \left(\frac{-1}{1}\right)^{24}=0$$

Calculate 5 to the power of 2 and get 25.

$$25w^{2}-18-7\times \left(\frac{-1}{1}\right)^{24}=0$$

Anything divided by one gives itself.

$$25w^{2}-18-7\left(-1\right)^{24}=0$$

Calculate -1 to the power of 24 and get 1.

$$25w^{2}-18-7\times 1=0$$

Multiply 7 and 1 to get 7.

$$25w^{2}-18-7=0$$

Subtract 7 from -18 to get -25.

$$25w^{2}-25=0$$

Add 25 to both sides. Anything plus zero gives itself.

$$25w^{2}=25$$

Divide both sides by 25.

$$w^{2}=\frac{25}{25}$$

Divide 25 by 25 to get 1.

$$w^{2}=1$$

Take the square root of both sides of the equation.

$$w=1 w=-1$$

Steps Using the Quadratic Formula

The opposite of -5w is 5w.

$$\left(\frac{5w}{1}\right)^{2}-18-7\times \left(\frac{-1}{1}\right)^{24}=0$$

Anything divided by one gives itself.

$$\left(5w\right)^{2}-18-7\times \left(\frac{-1}{1}\right)^{24}=0$$

Expand \left(5w\right)^{2}.

$$5^{2}w^{2}-18-7\times \left(\frac{-1}{1}\right)^{24}=0$$

Calculate 5 to the power of 2 and get 25.

$$25w^{2}-18-7\times \left(\frac{-1}{1}\right)^{24}=0$$

Anything divided by one gives itself.

$$25w^{2}-18-7\left(-1\right)^{24}=0$$

Calculate -1 to the power of 24 and get 1.

$$25w^{2}-18-7\times 1=0$$

Multiply 7 and 1 to get 7.

$$25w^{2}-18-7=0$$

Subtract 7 from -18 to get -25.

$$25w^{2}-25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 25 for a, 0 for b, and -25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$w=\frac{0±\sqrt{0^{2}-4\times 25\left(-25\right)}}{2\times 25}$$

Square 0.

$$w=\frac{0±\sqrt{-4\times 25\left(-25\right)}}{2\times 25}$$

Multiply -4 times 25.

$$w=\frac{0±\sqrt{-100\left(-25\right)}}{2\times 25}$$

Multiply -100 times -25.

$$w=\frac{0±\sqrt{2500}}{2\times 25}$$

Take the square root of 2500.

$$w=\frac{0±50}{2\times 25}$$

Multiply 2 times 25.

$$w=\frac{0±50}{50}$$

Now solve the equation w=\frac{0±50}{50} when ± is plus. Divide 50 by 50.

$$w=1$$

Now solve the equation w=\frac{0±50}{50} when ± is minus. Divide -50 by 50.

$$w=-1$$

The equation is now solved.

$$w=1 w=-1$$