Solve:

Question

Solve: $\sqrt{x} + \sqrt{x + 5} = 5$

Accepted Answer

Welcome back. I am so glad you're here. We are Given this equation the squared of X plus the square root of X plus seven equals seven. We want to solve for X. Well, it's a little bit tougher when X is inside that radical. And we're going to have to do a couple of separate square rings to let that X escape from its radical. And let's start off by letting it escape from this bigger radical first. So we'll square that one first in order to do that. We want to get that radical all by itself. On one side of the equation, I'm going to subtract the square root of X from both sides. So on the left we'll have the square root of X plus seven. And on the right that will equal seven minus the square root of X. Now we can square both sides. And that will bring that left hand side out of the radical. It's free. Yeah, it's just X plus seven over there now. And on the right. Well, we've got to foil this out. We have to write seven minus the square root of X times seven minus the square root of X. And we'll do our first seven times seven. That is 49. And our outside seven times negative squared of X. That's just minus seven. Square root of X. The inside it's the same thing negative squared of X times seven. So again minus seven squared of X. And our last negative squared of X. Times negative squared of X. Well negative times a negative is a positive. So plus the square root of X squared that still equals X plus seven. Now let's combine like terms in the middle here on the right hand side and will simplify this squirt of X squared. So bringing down that 49 and we have a negative seven X squared of X minus seven squared of X will be a minus 14 squared of X. And then plus the square root of X squared, that is just plus X. So now we've got X plus seven on the left hand side. Still let's bring over we're trying to get this squared of X by itself. So we're trying to bring over everything we can we'll subtract X from both sides and we'll subtract 49 From both sides. So on the left, the X's cancel out. We have 7 -49. So that's a negative 42 equals on the right. The 49 is gone. We've got negative 14 square root of X. And those Xs are gone great. We can divide both sides by negative 14, negative 42 divided by negative 14 is three. So we have three equals the square root of X. Yeah, we got that squared of X by itself. So now we can square both sides to get rid of that radical. So we now have nine equals x. We look at our answer choices and this matches with answer choice B Well done. We'll catch you on the next one

Solve: $\sqrt{x} + \sqrt{x + 5} = 5$

Key Concepts

Square Roots and Radicals

Isolating and Squaring Both Sides

Solving Quadratic Equations

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Solve: x+x+5=5\sqrt{x} + \sqrt{x + 5} = 5x+x+5=5

Key Concepts

Square Roots and Radicals

Isolating and Squaring Both Sides

Solving Quadratic Equations

Watch next

Solve: $\sqrt{x} + \sqrt{x + 5} = 5$