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DENIUS [597]
3 years ago
12

Solve the quadratic equation by completing the square. QUESTION ATTCHED BELOW!!!!!!!!!!

Mathematics
2 answers:
Maru [420]3 years ago
6 0

Answer:

{-6.59, -9.41}

Step-by-step explanation:

I like this problem. In order to start solving by completing the square, you need to get the left side in this form: a^2 + bx. Everything else needs to go to the other side of the equation. So step 1, subtract 62 from both sides. And the equation should look like x^2 + 16x = -62.

Then for step 2 you need to add (b/2)^2 to both sides. b is the 16 in our equation. So (16/2)^2 equals 64. So add 64 to both sides. So the equation should look like x^2 + 16x + 64 = 2. Now, you have completed the square and just need to factor for step 3. Because we completed the square, x^2 + 16 x + 64 will factor into the form (x + (b/2))^2. So it'll look like (x+8)^2 = 2. This is where you can click which form it is on your computer. It's addition, and fill in the numbers from left to right as 8 and 2. Step 4 is taking the square root of both sides. The square root on the left side will just cancel the square and leave you with x + 8, and the square root 2 - I would wait to simplify, so just leave it as x + 8 =

\sqrt{2}

For step 5, you need to isolate x by subtracting 8 from both sides. So now you should have x = \sqrt{2}

- 8. Now to simplify for step 6. Now in the calculator, type "sqr rt btn" 2 (close any parentheses at this point) and type minus 8. This is one solution - -6.59. Then, because you have a positive and negative solution from a square root, type neg. "sqr rt btn" 2 close parentheses for square root and neg if applicable, and type minus 8. and you should get -9.41 as your other solution. Now to go back and check out solutions, plug in one solution to x into the calculator and solve it. If the final statement is true, then the solution is true. then do same thing for other solution. Make sure they are rounded to the nearest hundredth as the directions read.

Mariulka [41]3 years ago
4 0

Answer:

x ≈ - 9.41, x ≈ - 6.59

Step-by-step explanation:

Given

x² + 16x + 62 = 0 ( subtract 62 from both sides )

x² + 16x = - 62

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(8)x + 64 = - 62 + 64

(x + 8)² = 2 ( take the square root of both sides )

x + 8 = ± \sqrt{2} ( subtract 8 from both sides )

x = - 8 ± \sqrt{2}

Hence

x = - 8 - \sqrt{2} ≈ - 9.41

x = - 8 + \sqrt{2} ≈ - 6.59

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Answer:

Step-by-step explanation:

5x + 2y = 20

Here we will show you how to calculate the following:

Calculate and show the solution for the x-intercept and y-intercept of 5x + 2y = 20.

Calculate the graph plot coordinates for 5x + 2y = 20

Solve 5x + 2y = 20 for x and also for y.

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The x-intercept is where the graph crosses the x-axis. To find the x-intercept, we set y1=0 and then solve for x.

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5x + 2(0) = 20

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The y-intercept is where the graph crosses the y-axis. To find the y-intercept, we set x2=0 and then solve for y.

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5(0) + 2y = 20

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Get Graph Plot Coordinates

Getting two graph points will allow you to make a straight line on a graph. The plot coordinate format is (x1,y1) and (x2,y2).

Thus, we use the x-intercept and y-intercept results above to get the graph plots for 5x + 2y = 20 as follows:

(x1,y1) and (x2,y2)

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Find slope

The slope of the line (m) is the steepness of the line. It is the change in the y coordinate divided by the corresponding change in the x coordinate. Simply plug in the coordinates from above and solve for m to get the slope for 5x + 2y = 20

m = (y2 - y1)/(x2 - x1)

m = (10 - 0)/(0 - 4)

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An expression may refer to any of the following:

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