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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.
What number would you add to both sides of x2 + 7x = 4 to complete the square?
Solution:
Given equation x2 + 7x = 4
We use the method completing the square to solve such equation.
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 + 7x = 4, the coefficient of the x term is 7. So (7/2)2 = 49/4
⇒ x2 + 7x +49/4 = 4 + 49/4
⇒ {4x2 + 28x + 49}/4 = {16 + 49} /4
⇒ {4x2 + 28x + 49} = 16 + 49
⇒ (2x + 7)2 = 65 [since a2+ 2ab + b2 = (a + b)2]
⇒ (2x + 7)2 = (√65)2
This looks like a perfect square, hence 49/4 should be added on both sides.
What number would you add to both sides of x2 + 7x = 4 to complete the square?
Summary:
The number 49/4 should be added on both sides of x2 + 7x = 4 to complete the square.
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