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4 years ago

How do I solve? Show with steps.

Mathematics

1 answer:

Ede4ka [16]4 years ago

8 0

Step-by-step explanation:

or,[(√-x-1)+(√x+9)]^2=4^2

or,(√-x-1)^2+2√(-x-1)(x+9)+(√x+9)^2=16

or,-x-1+2√-x^2-10x-9 +x+9=16

or,2√-x^2-10x-9=8

or,√-x^2-10x-9=4

squaring on both sides

or,-x^2-10x-9=16

or,-x^2-10x=25

or,-x(x+10)=25

Either,

x=-25 or, x=15.

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rosijanka [135]

Answer:

Step-by-step explanation:

To solve this equation, we need the formula for perfect squares:

$(a + b)^2 = a^2 + 2ab + b^2$

$(a - b)^2 = a^2 - 2ab + b^2$ <em>this is the formula we will use because the signs match the one in the question</em>.

Knowing these, we can set up an equation that assumes that the answer we will end up with is a perfect square.

Work:

$(v - x)^2 = v^2 -8v + x^2$

this is the setup for being able to solve for the unknown $x$ , now we need to solve for $x$ .

$(v - x)^2 = v^2 - 8v + x^2$ (I replaced $2ab$ with $8v$ because I'm setting up this question to be a perfect square).

$(v - x) (v - x) = v^2 - 8v + x^2$

multiply the left side. Remember that your answer will not be $v^2 + x^2$ , but $v^2 - 2vx +x^2$ .

$v^2 - 2vx + x^2 = v^2 + 8v + x^2$

Divide like terms and isolate the variable. In this case, $v^2$ and $x^2$ are on both sides, so dive them and they will be canceled out.

$2vx = 8v$

divide by $2v$ and you will have your value for $x$ .

$x = 4$

Now we plug $x$ into our original equation equation for perfect squares.

$(v - 4)^2 = v^2 - 8v + 16$

Our final answer is 16.

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4 years ago