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This is Raoul’s solution for the equation [tex]x^2-6x-27=0[/tex]:

**STEP 1:** [tex]x^2-6x-27=0[/tex]

**STEP 2:** [tex]x^2-6x-27+27=0+27[/tex]

**STEP 3:** [tex]x^2-6x+?=27+?[/tex]

**STEP 4:** [tex]x^2-6x+9=27+9[/tex]

**STEP 5:** [tex](x-3)^2=36[/tex]

**STEP 6:** [tex]\sqrt{(x-3)^2}=\sqrt{36}[/tex]

**STEP 7a:** [tex]x-3=6[/tex]

**STEP 8a:** [tex]x=9[/tex]

**STEP 7b:** [tex]x-3=-6[/tex]

**STEP 8b:** [tex]x=-3[/tex]

Answer :

The solution to the Raoul's equation x² - 6x - 27 = 0 is x = 9; or x = -3

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the equation:

x² - 6x - 27 = 0

Adding 27 to both sides:

x² - 6x - 27 + 27 = 0 + 27

x² - 6x = 27

Adding to both sides the square of half the coefficient of x, that is 9:

x² - 6x + 9 = 27 + 9

(x - 3)² = 36

taking square root of both sides:

√(x - 3)² = √36

x - 3 = ±6

x = 3 ± 6

x = 3 + 6 or; x = 3 - 6

x = 9; or x = -3

The solution to the Raoul's equation x² - 6x - 27 = 0 is x = 9; or x = -3

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