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#### In this article, you will learn how to solve any quadratic equation with the “Almighty” formula.

#### (Jump to Example)(Jump to Activity)

There are four different methods that can be used to solve a quadratic equation. Which are:

- Factorization;
- Completing the square;
- The general quadratic formula;
- Graphical solution.

Each of the four methods above can be used to solve specific types of quadratic equation, however our main focus shall be to apply the general quadratic formula also known as the “Almighty formula”.

As the alias implies, it can be used to solve any standard quadratic equation. This formula works where all else have failed.

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#### THE ALMIGHTY FORMULA (GENERAL QUADRATIC FORMULA)

A standard quadratic formula is of the form

ax^2 + bx + c = 0

Where:

a, b are coefficients of x^2 and x respectively;

c is a constant and;

a \ne 0

In solving for x, the formula states that:

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

SO, LET’S SEE AN EXAMPLE:**EXAMPLE :**

Solve the equation 2x^2 + 7x - 5 = 0 using the general quadratic(Almighty) formula.

**SOLUTION TO EXAMPLE:**

The equation is:

2x^2 + 7x - 5 = 0

So, that means:

a = 2, b = 7 and c = -5

Therefore, substituting the values of: a , b and c

into the formula x = \frac{-b\pm\sqrt{b^2-4ac}}{2a} gives:

x = \frac{-7\pm\sqrt{(7)^2-4(2)(-5)}}{2(2)}

x = \frac{-7\pm\sqrt{49-(-40)}}{4}

x = \frac{-7\pm\sqrt{49 + 40}}{4}

x = \frac{-7\pm\sqrt{89}}{4}

Hence:

x = \frac{-7\pm 9.43}{4}

x = \frac{-7 + 9.43}{4} OR x = \frac{-7 - 9.43}{4}

x = \frac{2.43}{4} OR x = \frac{-16.43}{4}

Final Answer:

x = 0.6075 OR x = -4.1075

**ACTIVITY:**

Solve the equation {2t^2 - 4t - 10 = 0} using the general quadratic(Almighty) formula.

## DILIGENTLY ATTEMPT TO SOLVE THE QUESTION FIRST. WHEN YOU ARE DONE, CLICK “VIEW SOLUTION NOW” TO SEE IF YOU GOT IT.

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**SOLUTION TO ACTIVITY:**

The equation is:

2t^2 - 4t - 10 = 0

This means that:

a = 2, b = -4 and c = -10

Therefore, substituting the values of a , b and c into the formula

t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Gives:

t = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(2)(-10)}}{2(2)}

Therefore:

t = \frac{4 \pm \sqrt{16 - (-80)}}{4}

t = \frac{4 \pm \sqrt{16 + 80}}{4}

= \frac{4 \pm \sqrt{96}}{4}

t = \frac{4 \pm 9.798}{4}

This implies that:

t = \frac{4 + 9.798}{4} OR t = \frac{4 - 9.798}{4}

t = \frac{13.798}{4} OR t = \frac{-5.798}{4}

FINAL ANSWER:

t = 3.45 OR t = -1.45