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Enter equation to graph, e.g. y=3x^2-1

Depdendent Variable

Number of equations to solve:

Equ. #1:

Equ. #2:

Equ. #3:

Equ. #4:

Equ. #5:

Equ. #6:

Equ. #7:

Equ. #8:

Equ. #9:

Solve for:

Enter inequality to solve, e.g. 2x+3>4

Enter inequality to graph, e.g. y<3x^2-1

Dependent Variable

Number of inequalities to solve:

Ineq. #1:

Ineq. #2:

Ineq. #3:

Ineq. #4:

Ineq. #5:

Ineq. #6:

Ineq. #7:

Ineq. #8:

Ineq. #9:

Solve for:

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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