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Use the quadratic formula to solve 2x^2 + 12x = -17. Show your work and explain your steps. If you do not explain or show your work, you will not receive credit.

Respuesta :

joseaaronlara

Answer:

The answer to your question is            x₁ = -3 + [tex]\frac{\sqrt{2}}{2}[/tex]    ;  x₂ = -3 [tex]- \frac{\sqrt{2}}{2}[/tex]

Step-by-step explanation:

Data

                     2x² + 12x = -17

Process

1.- Equal to zero

                   2x² + 12x + 17 = 0

2.- Identify a, b and c

a = 2

b = 12

c = 17

3.- Substitute in the general formula

                   x = [tex]\frac{-12 +- \sqrt{12^{2} -4(2)(17)}}{2(2)}[/tex]

4.- Simplify

                   x = [tex]\frac{-12 +- \sqrt{144 - 136}}{4}[/tex]

                   x = [tex]\frac{-12 +- \sqrt{8}}{4}[/tex]

                   x = [tex]\frac{-12 +-2 \sqrt{2}}{4}[/tex]

5.- Find x1 and x2

                  x₁ = -3 + [tex]\frac{\sqrt{2}}{2}[/tex]                        x₂ = -3 [tex]- \frac{\sqrt{2}}{2}[/tex]

Answer:

Step-by-step explanation:

The given quadratic equation is expressed as

2x² + 12x = - 17

Rearranging the equation so that it will be in the standard form of ax² + bx + c, it becomes

2x² + 12x + 17 = 0

The general formula for solving quadratic equations is expressed as

x = [- b ± √(b² - 4ac)]/2a

From the equation given,

a = 2

b = 12

c = 17

Therefore,

x = [- 12 ± √(12² - 4 × 2 × 17)]/2 × 1

x = [- 12 ± √(144- 136)]/2

x = [- 12 ± √8]/2

x = (- 12 + 2.83)/2 or x = (- 12 - 2.83)/2

x = 4.5 or x = 7.415

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