How Do You Complete the Square?
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Solving quadratics can be difficult. Completing the square is one method for solving a quadratic equation. A quadratic equation can also be solved by factoring, using the square roots, or using the quadratic formula. The cool thing is that solving quadratic equations by completing the square will always work when solving quadratic equations, and the technique is a good tool to have in your math tool belt.
How Do You Complete the Square?
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3 Responses to “How Do You Complete the Square?”
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You could have just used the equation
(b
-
2) ².
*^ that is supposed to say b over 2 squared. then you could have added whatever that equals to both sides after subtracting your k value. Then whatever was in the parenthesis before you squared it would equal (X+_)²=y you wouldn’t have to foil thus saving you 2 steps.
Heres how I solved it…
x²+8x+10=y (subtract 10)
-10=y-10
x²+8x=10-y
**heres where you do the equation I showed above**
(8÷2)²
(4)²
16
**add to both sides**
x²+8x=y-10
+16 +16
x²+8x+16=y+6
**instead of trying to find common factors that equal the equation above just use whatever you got in the ()**
(x+4)²=y-6 (add 6)
(x+4)²+6=y
^thats the answer you really dont have to solve with the ± considering from here you start to solve for the vertex since you just put the equation into vertex form from standard form….
vertex (-4,6)
line of symmetry x= -4
TADAAA shortcut.
Thanks for the alternate method.
Simplifying
4x^2 + 3x + -6 = y
Isolate the 1st 2 terms:
4x^2 + 3x + 0 = 6
Divide through by 4 to bring 1st term to x^2
x^2 + 3/4x + 0 = 6/4
Take half of the coefficient (don’t forget the sign!) of the x-term, and square it. Add this square to both sides of the equation.
x^2 + 3/4x + (3/8)^2 = 6/4 + (3/8)^2
Simplify
x^2 + 3/4x + 9/64 = 6/4 + 9/64
Place into standard form
(x + 3/8)^2 = 96/64 + 9/64
Combine Like terms
(x + 3/8)^2 = 105/64
Square-root both sides, remembering the “±” on the right-hand side. Simplify as necessary.
x + 3/8 = ±√105/8
Solve for x
Remember that the “±” means that you have two values for x.
x = -3/8 + √105/8
x = -3/8 – √105/8