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Quadratic equation

by Elizabeth Contrera
(Salinas, California, United States)










































Solve the following quadratic equation

x^2 + 6x = 9

your answer should include the complete solution set

Check the work by substituting your solutions for x into the original equation


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Dec 01, 2011
Quadratic Equation
by: Staff


Question:

by Elizabeth Contrera
(Salinas, California, United States)

x^2+6x=9


Answer:

x² + 6x = 9


You can solve this equation for x in a number of different ways.


Using the quadratic formula is probably the fastest way:

ax² + bx + c = 0

x = [-b ± √(b² - 4ac)]/(2a)


Rearrange your equation so that it is in the standard format for a quadratic equation (ax² + bx + c = 0).

x² + 6x = 9

x² + 6x - 9 = 9 – 9

x² + 6x - 9 = 0


x = unknown

a = 1

b = 6

c = -9


x = [-6 ± √(6² - 4*1*(-9))]/(2*1)

x = [-6 ± √(36 + 36)]/(2)

x = [-6 ± √(72)]/(2)

x = [-6 ± √(2*2²*3²)]/(2)

x = [-6 ± √(2²)*√(3²)*√(2)]/(2)

x = [-6 ± 2*3*√(2)]/(2)

x = [-6 ± 6*√(2)]/(2)

x = -6/2 ± [6*√(2)]/2

x = -3 ± 3*√(2)

x₁ = -3 + 3*√(2)

x₁ ≈ 1.2426406871193




x₂ = -3 - 3*√(2)

x₂ ≈ -7.2426406871193



the final answer is:


x ∈{-3 - 3*√(2), -3 + 3*√(2)}

or

x ∈{-7.2426406871193, 1.2426406871193}



Thanks for writing.

Staff
www.solving-math-problems.com



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