### About Quadratic Formula:

We previously learned how to solve any quadratic equation using the method known as: completing the square. We can use this process to create a general formula for solving any quadratic equation. This formula is known as the "Quadratic Formula".

Test Objectives

- Demonstrate the ability to write a quadratic equation in standard form
- Demonstrate the ability to identify a, b, and c in a quadratic equation
- Demonstrate the ability to solve a quadratic equation using the quadratic formula

#1:

Instructions: Solve each equation using the quadratic formula.

a) $$2x^2 + 11x + 12 = 0$$

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#2:

Instructions: Solve each equation using the quadratic formula.

a) $$6n^2 - 10n + 7 = 0$$

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#3:

Instructions: Solve each equation using the quadratic formula.

a) $$-10x^2 + 6 = 0$$

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#4:

Instructions: Solve each equation using the quadratic formula.

a) $$7x^2 = -11 + 10x + 5x^2$$

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#5:

Instructions: Solve each equation using the quadratic formula.

a) $$-p^2 - 10p - 25 = 0$$

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Written Solutions:

#1:

Solutions:

a) $$x = -\frac{3}{2}$$ or $$x = -4$$

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#2:

Solutions:

a) no real solution

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#3:

Solutions:

a) $$x = \frac{\pm\sqrt{15}}{5}$$

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#4:

Solutions:

a) $$x = \frac{5 \pm \sqrt{3}}{2}$$

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#5:

Solutions:

a) $$p = -5$$