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`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.
Luckily, we can transform any quadratic equation to the above form.
This transformation is called completing of square.
Rearrange: `ax^2 bx=-c` Divide throughout by `a`: `x^2 b/a x =-c/a` Write as a perfect square: `x^2 b/a x (b/(2a))^2=-c/a (b/(2a))^2` `(x b/(2a))^2=(-4ac b^2)/(4a^2)` Solve: `x b/(2a)= -sqrt(-4ac b^2)/(2a)` `x=-b/(2a) -sqrt(b^2-4ac)/(2a)` `x=(-b -sqrt(b^2-4ac))/(2a)` We'll use this result a great deal throughout the rest of the math we study.
Now, let us look at a useful application: solving Quadratic Equations ...
However, if your class covered completing the square, you should expect to be required to show that you can complete the square to solve a quadratic on the next test.
You can use the Mathway widget below to practice solving quadratic equations by completing the square.