Complete the square( A Level math UK-exam preparation questions)
Students will be able to complete quadratics to the square
If you pause the video and try to figure out , you’ll understand how to group the expression when necessary.
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Calculator Use
This calculator is a quadratic equation solver that will solve a second-order polynomial equation in the form ax2 + bx + c = 0 for x, where a ≠ 0, using the completing the square method.
The calculator solution will show work to solve a quadratic equation by completing the square to solve the entered equation for real and complex roots.
Completing the square when a is not 1
To complete the square when a is greater than 1 or less than 1 but not equal to 0, factor out the value of a from all other terms.
For example, find the solution by completing the square for:
2x2−12x+7=02x2−12x+7=0
a≠1,a=2a≠1,a=2 so divide through by 2
22x2−122x+72=0222x2−122x+72=02
which gives us
x2−6x+72=0x2−6x+72=0
Now, continue to solve this quadratic equation by completing the square method.
Completing the square when b = 0
When you do not have an x term because b is 0, you will have a easier equation to solve and only need to solve for the squared term.
For example: Solution by completing the square for:
x2+0x−4=0x2+0x−4=0
Eliminate b term with 0 to get:
x2−4=0x2−4=0
Keep xx terms on the left and move the constant to the right side by adding it on both sides
x2=4x2=4
Take the square root of both sides
x=±4–√x=±4
therefore
x=+2x=+2
x=−2