Solve By Completing The Square(Need Answer)?

By completing the square, we are trying to solve the particular variable in the equations above. I will give a step-by-step solution for each below:

1. x^2 + 8x + 15 = 0

There are three terms in this equation. One is constant (15) and the others contain variables (x^2 and 8x). Next, we take one of two approaches.

Our approach is to factor the equation by determining what two numbers multiplied together gives a result of 15 but when added give a sum of 8. 5 times 3 equals 15 and 5 plus 3 equal 8. The factored equation looks like this:

(x + 3)(x + 5) = 0 (a)

When the two are multiplied together using the First, Outside, Inside, Last (FOIL) method, it looks like this:

x^2 + 5x + 3x + 15 = 0 ----> x^2 + 8x + 15 = 0 (b)

Since the equation above (b) is equal to the starting equation (1.) after like terms are combined, we know that equation (a) is the correct method of factoring the equation.

Next, we break equation (a) into its terms and set each term equal to zero:

(x + 3) = 0 (c)

(x + 5) = 0 (d)

Now, solve each for x:

x + 3 = 0 (subtract 3 from each side)

x = -3

x + 5 = 0 (subtract 5 from each side)

x = -5

Our two possible solutions are that x is equal to -3 or -5. These values should be substitued in for x to see which maked equation 1 true.

Let's start with -3:

(-3)^2 + 8(-3) +15 = 0

(9) + (-24) + 15 = 0 This is a true statement so -3 is a solution.

Next, let's try -5:

(-5)^2 + 8(-5) + 15 = 0

(25) + (-40) + 15 =0 This is also a true statement so -5 is a solution.

The answer for equation 1. is that x is equal to -3 and -5

The rest of these are solved in the same way and I will give the factoring as well as the verification for each below:

2.) a^2 + 3a - 40 = 0

becomes:

(a + 8)(a - 5) = 0

a = -8

a = 5

verifying for -8:

(-8)^2 + 3(-8) - 40 = 0

(64) + (-24) - 40 = 0 True

verifying for 5:

(5)^2 + 3(5) - 40 = 0

(25) + 15 - 40 = 0 True

3.) y^2 + 4y - 45 = 0

becomes:

(y - 9)(y + 5) = 0

y = -9

y = 5

verifying for -9:

(-9)^2 + 4(-9) - 45 = 0

(81) + (-36) - 45 = 0 True

verifying for 5:

(5)^2 + 4(5) - 45 = 0

(25) + (20) - 45 = 0 True

4.) 3x^2 - 7x - 6 = 0

becomes:

(3x + 2)(x - 3) = 0

x = -2/3

x = 3

verify for -2/3:

3(2/3)^2 - 7(-2/3) - 6 = 0

3(4/9) + (14/3) - 6 = 0

(12/9) + (14/3) - 6 = 0

(4/3) + (14/3) - (18/3) = 0 True

verify for 3:

3(3)^2 - 7(3) - 6 = 0

3(9) - 21 - 6 = 0

27 - 21 - 6 = 0 True

1)

x^2+8x= -15

then you must find: (b/2)^2 because the answer to this formula will provide you with the number that makes a perfect square trinomial.

(8/2)^2= 16

then: you would add 16 to both sides.

x^2+8x+16= -15+16

it's now easy to factor the perfect square trinomial.

(x+4)^2= 1

In order to isolate the x, you would need to first square root the 1 which gives you:

x+4= +/-1

subtract 4 from both sides for both solutions:

x= -1-4= -5

x= 1-4= -3

That's how you complete the square. The method the person above me used was factorizing. I don't want to solve the rest for you because I would be depriving you of learning how to get the answers yourself.

1. (x+5)(x+3) or x=-3

2. (a-5)(a+8) or a=-8

3. (y+9)(y-5) or y=-9

4. (3x-2)(x+3) or x= -2/3

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