This calculator solves quadratic equations. You can solve equations by completing the square or by using quadratic formula. The calculator will write down complete solution. Every step will be explained in detail.

A general quadratic equation can be written in the form $ax^2 + bx + c = 0$. This calculator solves quadratic equation using two methods.
When $a \ne 0$ , there are two solutions to $ax^2 + bx + c = 0$ and they are
$$x = \frac{b \pm \sqrt{b^24ac}}{2a}.$$The formula can be used to solve any quadratic equation.
Example:
Solve equation $2x^2 + 7x  15 = 0$ using the quadratic formula.
Solution:
Here we have : $ a = 2 ~ b = 7 ~ c = 15 $
To calculate first solution we use "+" sign: 
To calculate second solution we use "" sign: 
$$x_{1} = \frac{7 + 13} {4}$$
$$x_{1} = \frac{6}{4}$$
$$x_{1} = \frac{3}{2}$$

$$x_{2} = \frac{7  13} {4}$$
$$x_{2} = \frac{20} {4}$$
$$x_{2} = 5$$

Exercise:
Solve equation 3x^{2} + 2x  5 = 0. ( Use above calculator to check your solution. )
The best way to learn this method is by using an example.
Example:
Solve equation 2x^{2} + 7x  15 = 0 by completing the square.
Solution:
$$2x^2 + 7x  15 = 0$$


$$2x^2 + 7x  15 = 0 / : 2$$
$$x^2 + \frac{7}{2}x  \frac{15}{2} = 0$$

Step1: Divide all terms by the coefficient of x^{2}. 
$$x^2 + \frac{7}{2}x = \frac{15}{2}$$

Step 2: Keep all terms containing x on one side. Move the constant to the right. 
$$x^2 + \frac{7}{2}x + {\left(\frac{7}{4}\right)}^2= \frac{15}{2}+{\left(\frac{7}{4}\right)}^2$$

Step 3: Take half of the xterm coefficient and square it. Add this value to both sides. 
$$x^2 + \frac{7}{2}x + {\left(\frac{7}{4}\right)}^2= \frac{169}{16}$$

Step 4: Simplify right side. 
$$ {\left(x + \frac{7}{4}\right)}^2= \frac{169}{16}$$

Step 5: Write the perfect square on the left. 
$$ x + \frac{7}{4}= \pm\sqrt{\frac{169}{16}}$$
$$ x + \frac{7}{4}= \pm\frac{13}{4}$$

Step 6: Take the square root on both sides of the equation. 
$$ x_1 =  \frac{7}{4} + \frac{13}{4} = \frac{3}{2}$$
$$ x_2 =  \frac{7}{4}  \frac{13}{4} = 5$$

Step 7: Solve for x. 
Exercise:
Solve equation x^{2}  4x + 3 = 0. ( Use above calculator to check your solution. )
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