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A number is 30 less than its square. Find all such numbers.

-5,6

Algebra

Chapter 6

Polynomial Factorizations and Equations

Section 7

Applications of Polynomial Equations

Graphs and Statistics

Exponents and Polynomials

Equations and Inequalities

Polynomials

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Lectures

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all right, The first this question that we're going to be going over is Oh, a number. A number is 30 less van. Then it's square. So we're trying to prove that a number is 30 less than its square. And to to start this, we're gonna let we're gonna let, um, x equal a number. Just any number. Ah, and then So this number has to be equal to it's square minus 30. So if we we see this and we're gonna set those sides equal to zero, so it's gonna be zero equals X squared minus X minus 30. Because we brought this X and we put it over on this side. So now we have the equation. Zero equals x squared minus X minus 30. This is an equation that we can factor. Um, so we're gonna look at really what numbers we can factor in what products we can get. So we get, um, zero equals, if we break up the the factor were able to get, we have negative 30 which breaks up into five and negative six. And when you add these together, the equal negative one. So these are going to be our factors so weaken were able to simply factor to make it X plus five and then x minus six. So the number we look here x is equal to negative five. And in this bracket, X is equal to six. So therefore, this symbol, the three dots means therefore therefore the number could, I should say, could be either negative five or six. So either negative five or six satisfies this equation. Um, so that would be the answer to this question.

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