how to do completing square method
Answers
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Answer:
3/4, -1
Step-by-step explanation:
What is completing square method:
It is a method used to solve a Quadratic equation by changing the form of the equation so that the left hand is a perfect square trinomial.
Example:
Solve 4x² + x - 3 = 0 by completing the square method:
(i) Move the constant to RHS:
Given Equation is 4x² + x - 3 = 0
It can be written as 4x² + x = 3.
(ii) Coefficient of x² should be 1:
So, the Equation is 4x² + x = 3.
Divide the entire Equation by the coefficient of x², we get
⇒ x² + (x/4) = 3/4
(iii) Add the square of half the coefficient of 'x' on both sides:
x² + 2(x)(1/4) + (1/8)² = (3/4) + (1/64)
(x + 1/8)² = 49/64
(iv) Solve for x by simplification:
(x + 1/8) = ±7/8.
(a)
When x + 1/8 = 7/8
⇒ x = 7/8 - 1/8
⇒ x = 6/8
⇒ x = 3/4
(b)
When x + 1/8 = -7/8
⇒ x = -7/8 - 1/8
⇒ x = -8/8
⇒ x = -1
Therefore x = 3/4, -1 are the roots of the equation.
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