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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
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# Solving Quadratic Equations by Completing the Square

Example

Solve by completing the square: 3x2 - 30 = -21x

Solution

 Step 1 Isolate the x2-term and the x-term on one side of the equation. Add 21x to both sides. Add 30 to both sides. 3x2 - 30 = -21x 3x2 + 21x - 30 = 0 3x2 + 21x = 30 Step 2 If the coefficient of x2 is not 1, divide both sides of the equation by the coefficient of x2. Divide both sides by 3. x2 + 7x = 10 Step 3 Find the number that completes the square: Multiply the coefficient of x by . Square the result. The coefficient of the x-term is 7. Step 4 Add the result of Step 3 to both sides of the equation. Add to both sides. Simplify the right side. The result is . Step 5 Write the trinomial as the square of a binomial. Step 6 Finish solving using the Square Root Property.Use the Square Root Property. For each equation, subtract from both sides and simplify the radical. Step 7 Check each solution. We leave the check for you.
The solutions of 3x2 - 30 = -21x are

Note:

To divide both sides of an equation by 3, we divide each term by 3, like this:

We can use the â€œplus or minusâ€ symbol to write the solutions like this