completing square method of quadratic equation.. example and explaination
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Answers
Answer:
What is Completing the Square?
Completing the square is a method of solving quadratic equations that we cannot factorize.
Completing the square means manipulating the form of the equation so that the left side of the equation is a perfect square trinomial.
How to Complete the Square?
To solve a quadratic equation; ax2 + bx + c = 0 by completing the square.
The following are the procedures:
Manipulate the equation in the form such that the c is alone on the right side.
If the leading coefficient a is not equals to 1, then divide each term of the equation by a such that the co-efficient of x2 is 1.
Add both sides of the equation by the square of half of the co-efficient of term-x
⟹ (b/2a)2.
Factor the left side of the equation as the square of the binomial.
Find the square root of both sides of the equation. Apply the rule (x + q) 2 = r, where
x + q= ± √r
Solve for variable x
Complete the square formula
In mathematics, completing the square is used to compute quadratic polynomials. Completing the Square Formula is given as: ax2 + bx + c ⇒ (x + p)2 + constant.
The quadratic formula is derived using a method of completing the square. Let’s see.
Given a quadratic equation ax2 + bx + c = 0;
Isolate the term c to right side of the equation
ax2 + bx = -c
Divide each term by a.
x2 + bx/a = -c/a
Write as a perfect square
x 2 + bx/a + (b/2a)2 = – c/a + (b/2a)2
(x + b/2a) 2= (-4ac+b2)/4a2
(x + b/2a) = ±√ (-4ac+b2)/2a
x = – b/2a ±√ (b2– 4ac)/2a
x = [- b ±√ (b2– 4ac)]/2a………. (This is the quadratic formula)
Now let’s solve a couple of quadratic equations using the completing square method.
Example 1
Solve the following quadrating equation by completing square method:
x2 + 6x – 2 = 0
Solution
Transform the equation x2 + 6x – 2 = 0 to (x + 3)2 – 11 = 0
Since (x + 3)2 =11
x + 3 = +√11 or x + 3 = -√11
x = -3+√11
OR
x = -3 -√11
But √11 =3.317
Therefore, x = -3 +3.317 or x = -3 -3.317,
x = 0.317 or x = -6.317
Step-by-step explanation:
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