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# Please, this topic makes no sense...

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If $x^2 - 7x + c = (x + a)^2$for some constants $a$ and $c,$ then find $a.$

If $x^2 - 7x + c = (x + a)^2$for some constants $a$ and $c,$ then find $c.$

If you complete the square on the equation $x^2 + 10x = 9,$you will get an equation of the form "$(x + r)^2 = c$".

For what real values of $a$ is $x^2 + ax + 25$ the square of a binomial? If you find more than one, then list the values separated by commas.

Find all real solutions to$100x^2+20x+1=16.$

Find all real values of $x$ that satisfy the equation $(x^2 - 82)^2 = 324$. If you find more than one, then list the values separated by commas.

Find the smallest real value of $x$ such that $x^2+6x + 9 = 24$.

Find the roots of $x^2 + 12x + 36 + 25 = 0.$

Dec 20, 2020

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I think that presentation is confusing too!

Try expanding this    $$(x+7)^2$$  and you will get     $$x^2+17x+49$$

Do it to make sure you know how and to check I did it right.

so I have    $$x^2+14x+49=(x+7)^2$$

Notice if I half the 14 I get 7

If I square the 7 I git 49

so

$$x^2+14x+(\frac{14}{2})^2=(x+\frac{14}{2})^2$$

$$​​​​$$

If there is no number in front of the x^2 except for an invisible 1 then this will always be true.

$$x^2 - 7x + c = (x + a)^2$$

c will be  half of -7

a will be (half of -7) squared.

So you complete this bit for me please.

Dec 20, 2020