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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 + 6x = 7 by completing the square. What is the solution set of the equation?
Solution:
Given equation x2 +6x = 7
Using the method of completing the square, let us find the solution set that satisfies the 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.
Step 1: Rearrange the equation in the form of ax2 + bx = c, if necessary.
⇒ x2 + 6x = 7
Step 2: Add (b/ 2)2 on both the sides of the equation, b = 6 (coefficient of x)
⇒ x2 + 6x + (6/ 2)2 = 7 + (6/ 2)2
Step 3: Factorize the sides using algebraic identity (a + b)2 into perfect squares.
⇒ (x + 3 )2 = 7 + (3)2
Step 4: Take square root on both the sides.
⇒ √ (x + 3 )2 = √ 16
Step 5: Solve for x.
⇒ x + 3 = ± 4
⇒ x = ± 4 - 3
⇒ x = - 7 or 1
Thus the solution set is {-7,1}
Solve x2 + 6x = 7 by completing the square. What is the solution set of the equation?
Summary:
By solving x2 + 6x = 7 by completing the square, we get thea solution set as {-7, 1}.
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