Solve by completing the square ( find the vertex only)
K^2-18k+50=0
M^2+500m+100=0
Recall that (x-a)^2 = x^2-2ax+a^2
k^2-18k+50 = 0
k^2-18k = -50
Now, you want half of the coefficient of k and square it, so you have a perfect square. Then, to keep things equal, you have to add it to the right side as well.
k^2-18k+81 = -50+81
(k-9)^2 = 31
k-9 = ±√31
k = 9±√31
Now do the other the same way.
Uhhggf
To solve quadratic equations by completing the square, follow these steps:
1. Write the equation in the form: ax^2 + bx + c = 0.
For the first equation: K^2 - 18k + 50 = 0, we already have it in this form with a = 1, b = -18, and c = 50.
2. Move the constant term (c) to the right side of the equation, leaving space to complete the square.
K^2 - 18k = -50
3. Take half of the coefficient of the x-term (b) and square it.
For the first equation: b = -18, half of -18 is -9, and (-9)^2 = 81.
4. Add the squared term from step 3 to both sides of the equation.
K^2 - 18k + 81 = -50 + 81
Simplify:
(K - 9)^2 = 31
5. Rewrite the equation in vertex form: (x - h)^2 = k.
For the first equation, the vertex form is:
(K - 9)^2 = 31
Comparing this form with the general form (x - h)^2 = k, we can see that the vertex (h, k) is (9, 31).
Now, let's solve the second equation:
1. Write the equation in the form: ax^2 + bx + c = 0.
For the second equation: M^2 + 500m + 100 = 0, we already have it in this form with a = 1, b = 500, and c = 100.
2. Move the constant term (c) to the right side of the equation, leaving space to complete the square.
M^2 + 500m = -100
3. Take half of the coefficient of the x-term (b) and square it.
For the second equation: b = 500, half of 500 is 250, and (250)^2 = 62500.
4. Add the squared term from step 3 to both sides of the equation.
M^2 + 500m + 62500 = -100 + 62500
Simplify:
(M + 250)^2 = 62400
5. Rewrite the equation in vertex form: (x - h)^2 = k.
For the second equation, the vertex form is:
(M + 250)^2 = 62400
Comparing this form with the general form (x - h)^2 = k, we can see that the vertex (h, k) is (-250, 62400).
So, for the first equation, the vertex is (9, 31), and for the second equation, the vertex is (-250, 62400).