Solve p-1=sqrt{50-2p}

$$p - 1 = \sqrt { 50 - 2 p }$$

Solve for p

$$p=7$$

Solution Steps

Square both sides of the equation.

$$\left(p-1\right)^{2}=\left(\sqrt{50-2p}\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(p-1\right)^{2}.

$$p^{2}-2p+1=\left(\sqrt{50-2p}\right)^{2}$$

Calculate \sqrt{50-2p} to the power of 2 and get 50-2p.

$$p^{2}-2p+1=50-2p$$

Subtract 50 from both sides.

$$p^{2}-2p+1-50=-2p$$

Subtract 50 from 1 to get -49.

$$p^{2}-2p-49=-2p$$

Add 2p to both sides.

$$p^{2}-2p-49+2p=0$$

Combine -2p and 2p to get 0.

$$p^{2}-49=0$$

Consider p^{2}-49. Rewrite p^{2}-49 as p^{2}-7^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(p-7\right)\left(p+7\right)=0$$

To find equation solutions, solve p-7=0 and p+7=0.

$$p=7 p=-7$$

Substitute 7 for p in the equation p-1=\sqrt{50-2p}.

$$7-1=\sqrt{50-2\times 7}$$

Simplify. The value p=7 satisfies the equation.

$$6=6$$

Substitute -7 for p in the equation p-1=\sqrt{50-2p}.

$$-7-1=\sqrt{50-2\left(-7\right)}$$

Simplify. The value p=-7 does not satisfy the equation because the left and the right hand side have opposite signs.

$$-8=8$$

Equation p-1=\sqrt{50-2p} has a unique solution.

$$p=7$$