Solving Quadratic Equations By Completing The Square Practice Problems

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Then click the button and select "Solve by completing the square" to compare your answer to Mathway's.

`x^2 x/4 (1/8)^2=3/4 (1/8)^2` `x^2 x/4 1/64=3/4 1/64` Step (iv) Write the left side as a square and simplify the right side.

`(x 1/8)^2=(48 1)/64=49/64` Step (v) Equate and solve `x 1/8= -sqrt(49/64)= -7/8` So `2s^2 5s=3` Divide throughout by 2.

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`(s 5/4)^2=3/2 25/16=(24 25)/16=49/16` Solve for `s`.

`s 5/4= -sqrt(49/16)` `s=-5/4 -7/4=(-12)/4\ "or"\ 2/4` `s=-3\ text(or)\ 1/2` `3x^2=3-4x` Rearrange: `3x^2 4x=3` Divide throughout by 3: `x^2 4/3x=1` Write left hand side as a perfect square: `x^2 4/3x (2/3)^2=1 (2/3)^2` `(x 2/3)^2=1 4/9=13/9` Solve: `x 2/3= -sqrt(13/9)= -sqrt(13)/3` `x=-2/3 -sqrt(13)/3` `x=-1.869\ "or"\ x=0.535` `9v^2-6v-2=0` Rearrange: `9v^2-6v=2` Divide throughout by 9: `v^2-2/3v=2/9` Write as a perfect square: `v^2-2/3v (1/3)^2=2/9 (1/3)^2` `(v-1/3)^2=2/9 1/9=1/3` Solve: `v-1/3 = -sqrt(1/3)` `v=1/3 -sqrt(1/3)` `v=-0.244\ "or"\ v=0.911` `ax^2 bx c=0` This is a general quadratic equation.

By the way, unless you're told that you to use completing the square, you will probably never use this method in actual practice when solving quadratic equations.

Either some other method (such as factoring) will be obvious and quicker, or else the Quadratic Formula (reviewed next) will be easier to use.

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