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the square of a number plus three times the number is 70. find the numbers.

Sagot :

Luv2Teach

Answer:

Step-by-step explanation:

The equation for that is

[tex]x^2+3x=70[/tex]

If we subtract over the 70, we have a quadratic that we can factor to solve for the values of x that will make that equation true.

[tex]x^2+3x-70=0[/tex]

Now we need the factors of 70 that will either add or subtract to give us the linear term of 3. The factors of 70 that will work are 10 and 7. 10 times 7 is 70, and 10 - 7 = 3:

[tex]x^2+10x-7x-70=0[/tex] and now we will factor by grouping:

[tex](x^2+10x)-(7x-70)=0[/tex] and factor out what's common:

[tex]x(x+10)-7(x+10)=0[/tex]

The factor (x + 10) is common, so we will now factor that out:

[tex](x+10)(x-7)=0[/tex]

By the Zero Product Property, either x + 10 = 0 or x - 7 = 0, so x = -10 or 7

Those are the 2 numbers that will work.

[tex](-10)^2+3(-10)=70[/tex] simplifies to

100 - 30 which does in fact equal 70. OR

[tex](7)^2+3(7)=70[/tex] which simplifies to

49 + 21 which also equals 70.

So you're done!

onyebuchinnaji

The values of the unknown number is 7 or - 10

The given expression from words to algebra;

let the unknown number = n

the square of the number = n²

three times the number = 3n

n² + 3n = 70

To find:

  • the values of n

The values of n is calculated as follows;

[tex]n^2 + 3n = 70\\\\n^2 + 3n - 70 = 0\\\\factorize \ the \ equation;\\\\n^2 + 10n - 7n - 70 = 0\\\\n(n + 10) - 7(n + 10) = 0\\\\(n-7)(n+ 10) = 0\\\\n = 7 \ or \ - 10[/tex]

Thus, the values of the unknown number is 7 or - 10

Learn more here: https://brainly.com/question/16889590

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