Solve w=sqrt{9w-20}

$$w = \sqrt { 9 w - 20 }$$

Solve for w

$$w=5$$

$$w=4$$

Solution Steps

Square both sides of the equation.

$$w^{2}=\left(\sqrt{9w-20}\right)^{2}$$

Calculate \sqrt{9w-20} to the power of 2 and get 9w-20.

$$w^{2}=9w-20$$

Subtract 9w from both sides.

$$w^{2}-9w=-20$$

Add 20 to both sides.

$$w^{2}-9w+20=0$$

To solve the equation, factor w^{2}-9w+20 using formula w^{2}+\left(a+b\right)w+ab=\left(w+a\right)\left(w+b\right). To find a and b, set up a system to be solved.

$$a+b=-9 ab=20$$

Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. List all such integer pairs that give product 20.

$$-1,-20 -2,-10 -4,-5$$

Calculate the sum for each pair.

$$-1-20=-21 -2-10=-12 -4-5=-9$$

The solution is the pair that gives sum -9.

$$a=-5 b=-4$$

Rewrite factored expression \left(w+a\right)\left(w+b\right) using the obtained values.

$$\left(w-5\right)\left(w-4\right)$$

To find equation solutions, solve w-5=0 and w-4=0.

$$w=5 w=4$$

Substitute 5 for w in the equation w=\sqrt{9w-20}.

$$5=\sqrt{9\times 5-20}$$

Simplify. The value w=5 satisfies the equation.

$$5=5$$

Substitute 4 for w in the equation w=\sqrt{9w-20}.

$$4=\sqrt{9\times 4-20}$$

Simplify. The value w=4 satisfies the equation.

$$4=4$$

List all solutions of w=\sqrt{9w-20}.

$$w=5 w=4$$