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1 year ago

Solve x2 + 6x = 7 by completing the square. Which is the solution set of the equation?

Mathematics

2 answers:

Doss [256]1 year ago

8 0

Answer:

x = 1; x = -7

Step-by-step explanation:

Given

x^2 + 6x = 7

we want to complete the square. If we have (x + a)^2 and expand it we get: x^2 + 2ax + a^2. The second term in the equation suggest that 2ax = 6x or a = 3. Then, adding 3^2 at both sides of the equation of the problem:

x^2 + 6x + 3^2 = 7 + 3^2

(x + 3)^2 = 16

x + 3 = sqrt(16)

That gives us two options

x + 3 = 4

x = 1

x + 3 = -4

x = -7

Ber [7]1 year ago

7 0

So first you have to find the perfect square that matches up with x^2 + 6x

so half of 6, and square it. your perfect square is 9

x^2 + 6x + 9 = 7 + 9

then, condense the left side of the equation into a squared binomial:

(x + 3)^2 = 16

take the square root of both sides:

x + 3 = ± √16

therefore:

x + 3 = ± 4

x = - 3 ± 4

so your solution set is:

x = 1, -7

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1 year ago

Determine if each of the following sets is a subspace of ℙn, for an appropriate value of n. Type "yes" or "no" for each answer.

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Answer:

1. Yes.

2. No.

3. Yes.

Step-by-step explanation:

Consider the following subsets of Pn given by

1.Let W1 be the set of all polynomials of the form $p(t)=at^2$ , where a is in ℝ.

2.Let W2 be the set of all polynomials of the form $p(t)=t^2+a$ , where a is in ℝ.

3. Let W3 be the set of all polynomials of the form $p(t)=at^2+at$ , where a is in ℝ.

Recall that given a vector space V, a subset W of V is a subspace if the following criteria hold:

- The 0 vector of V is in W.

- Given v,w in W then v+w is in W.

- Given v in W and a a real number, then av is in W.

So, for us to check if the three subsets are a subset of Pn, we must check the three criteria.

- First property:

Note that for W2, for any value of a, the polynomial we get is not the zero polynomial. Hence the first criteria is not met. Then, W2 is not a subspace of Pn.

For W1 and W3, note that if a= 0, then we have p(t) =0, so the zero polynomial is in W1 and W3.

- Second property:

W1. Consider two elements in W1, say, consider a,b different non-zero real numbers and consider the polynomials

$p_1 (t) = at^2, p_2(t)=bt^2$ .