When the sum of 1 and twice a negative number is subtracted from ...

Question

When the sum of 1 and twice a negative number is subtracted from twice the square of the number, 0 results. Find the number.

Accepted Answer

Welcome back. I'm so glad you're here. We've got this sentence that we need to turn into an equation. So when the difference between a number, well, whenever we see a number we're going to use X. So the difference between that means we're going to be subtracting difference between a number X and 12. So we're going to subtract X minus 12 0. And when the difference between X and 12 is doubled, that means we're going to put this in parentheses and multiply it by two and added to. Well, that means we're going to add the square of that number. Okay, that number is X. But the square of that number is going to be X squared. It results in zero. Well that means it's going to equal zero there. We've turned it into an equation. Now we just need to solve for X. Let's go ahead and distribute that to to what's inside the parentheses two times X is two X. Two times negative 12 is negative 24. Bring down the plus X squared equals zero. Now let's rewrite this so that our X squared is in front, X squared plus two. X minus 24 equals zero. And now we can factor this what times what gives us X squared? That's X times X. What two factors when multiplied? Give us a negative 24 when added give us a positive two, that's going to be plus six and minus four. Now we can set these two factors equal to zero, X plus six equals zero and X minus four equals zero for X plus six equals zero, Let's subtract six from both sides. So we've got X equals negative six for one solution, and let's add four to both sides for x minus four equals zero, which will give us X equals four for our other solution. We look at our answer choices and this matches with answer choice. A well done, we'll catch you on the next one.

When the sum of 1 and twice a negative number is subtracted from twice the square of the number, 0 results. Find the number.

Key Concepts

Algebraic Expressions

Quadratic Equations

Solving Equations

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