## anonymous one year ago x^2+5x-24 = 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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1. alekos

Are you attempting to solve for x using the complete the square method?

2. anonymous

I'm trying to get the sum of 2 solutions of the equation $X^{2}+5x-24=0$

3. alekos

you mean the product of two solutions, in other words you want to factorise the quadratic

4. alekos

(x+a)(x+b) = x^2 +5x -24

5. mathstudent55

Solve 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.

6. alekos

Hmm. I don't get -5 as one of the solutions?

7. mathstudent55

Step 1. Let's solve the quadratic equation using the complete the square method. $$x^2+5x-24 ~~~= ~~~0$$ $$~~~~~~~~~~~~+24~~~~+24$$ -------------------- $$x^2 + 5x ~~~~~~~~~~=~~24$$ The complete the square step is to add the square of half of the x-term coefficient. The x-term 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.

8. mathstudent55

$$x^2 + 5x + \dfrac{25}{4} = 24 + \dfrac{25}{4}$$ $$x^2 + 5x + \dfrac{25}{4} = \dfrac{96}{4} + \dfrac{25}{4}$$ $$x^2 + 5x + \dfrac{25}{4} = \dfrac{121}{4}$$ $$\left( x + \dfrac{5}{2} \right)^2 = \dfrac{121}{4}$$ We have finished the step of completing the square. Now we take the square root of both sides.

9. mathstudent55

Step 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.

10. mathstudent55

$$\left( x + \dfrac{5}{2} \right)^2 = \dfrac{121}{4}$$ $$x + \dfrac{5}{2} = \pm\sqrt{\dfrac{121}{4}}$$ 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: $$3 + (-8) = -5$$