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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
Solve x2 + 8x = 33 by completing the square. Which is the solution set of the equation?
{-11, 3}, {-3, 11}, {-4, 4}, {-7, 7}
Solution:
Given equation x2 + 8x = 33
We complete the square for making the LHS into a perfect square trinomial.
- Divide the coefficient of the x term by 2 then square the result.
- This number will be added to both sides of the equation.
For the quadratic equation x2 - 8x = 3, the coefficient of the x term is 8
So (8/2)2 = (4)2 = 16
⇒ x2 + 8x +16 = 33 + 16
⇒ x2 + 2(4)(x) + 16 = 49
⇒ {x2 + 2(x)(4) + 42} = 49 [ since a2 + 2ab + b2 = (a + b)2]
⇒ (x + 4)2 = 49
Applying square root on both sides, we get
⇒ x + 4 = √49
⇒x = ±7 - 4
⇒ x = -11, 3
The solution set is {-11, 3}
Solve x2 + 8x = 33 by completing the square. Which is the solution set of the equation?
Summary:
By solving the equation x2 + 8x = 33 by completing the square, we get solution set as {-11, 3}.
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