This calculator solves quadratic equations by completing the square or by using quadratic formula. It displays the work process and the detailed explanation. 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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