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anonymous
 one year ago
x^2+5x24 = 0
+ 24 +24
x^2+5x=24
Then I know you square root both sides but that's when I get stuck, I'm thinking it would then be something like
x + ? = 2sqrt6
The answer is 5 so I just need help being taught how to do these last steps, unless I'm completely wrong in the beginning steps.
anonymous
 one year ago
x^2+5x24 = 0 + 24 +24 x^2+5x=24 Then I know you square root both sides but that's when I get stuck, I'm thinking it would then be something like x + ? = 2sqrt6 The answer is 5 so I just need help being taught how to do these last steps, unless I'm completely wrong in the beginning steps.

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alekos
 one year ago
Best ResponseYou've already chosen the best response.0Are you attempting to solve for x using the complete the square method?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm trying to get the sum of 2 solutions of the equation \[X^{2}+5x24=0\]

alekos
 one year ago
Best ResponseYou've already chosen the best response.0you mean the product of two solutions, in other words you want to factorise the quadratic

alekos
 one year ago
Best ResponseYou've already chosen the best response.0(x+a)(x+b) = x^2 +5x 24

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0Solve the equation using the complete the square method. Then add the two solutions together. The final answer is indeed 5. Now just explain how to do it.

alekos
 one year ago
Best ResponseYou've already chosen the best response.0Hmm. I don't get 5 as one of the solutions?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0Step 1. Let's solve the quadratic equation using the complete the square method. \(x^2+5x24 ~~~= ~~~0\) \(~~~~~~~~~~~~+24~~~~+24\)  \(x^2 + 5x ~~~~~~~~~~=~~24\) The complete the square step is to add the square of half of the xterm coefficient. The xterm coefficient is 5. Half of 5 is \(\dfrac{5}{2} \). The square of \(\dfrac{5}{2} \) is \(\dfrac{25}{4} \). We add \(\dfrac{25}{4} \) to both sides to complete the square.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0\(x^2 + 5x + \dfrac{25}{4} = 24 + \dfrac{25}{4} \) \(x^2 + 5x + \dfrac{25}{4} = \dfrac{96}{4} + \dfrac{25}{4} \) \(x^2 + 5x + \dfrac{25}{4} = \dfrac{121}{4}\) \(\left( x + \dfrac{5}{2} \right)^2 = \dfrac{121}{4} \) We have finished the step of completing the square. Now we take the square root of both sides.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0Step 2. Take square root of both sides. Rule: If \(x^2 = k\), where \(k\) is a number, then \(x = \pm k\). Because of the rule above, we must be careful to include both the positive and negative roots of the number on the right side of the equal sign.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0\(\left( x + \dfrac{5}{2} \right)^2 = \dfrac{121}{4}\) \( x + \dfrac{5}{2} = \pm\sqrt{\dfrac{121}{4}}\) Notice the \(\pm\) sign on the right side. Step 3. Separate the equations and solve for x. \( x + \dfrac{5}{2} = \pm \dfrac{11}{2}\) Now we separate the above into two equations, one for the positive root, and one for the negative root. \(x + \dfrac{5}{2} = \dfrac{11}{2}\) or \(x + \dfrac{5}{2} = \dfrac{11}{2}\) \(x = \dfrac{6}{2}\) or \(x = \dfrac{16}{2}\) \(x = 3\) or \(x = 8\) The solutions to the quadratic equation are 3 and 8. When we add the solutions, we get: \(3 + (8) = 5\)
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