Solve the Quadratic Equation: x² - 36 = 6x - 36

Solve the following equation:

x2−36=6x−36 x^2-36=6x-36

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find X
00:03 Factor 36 into 6 squared
00:10 Factor 36 into factors 6 and 6
00:18 Take out the common factor from parentheses
00:28 Use the shortened multiplication formulas
00:40 Use the shortened multiplication formulas and build a trinomial
00:45 Divide by the common factor
01:00 Reduce what is possible
01:03 Isolate X
01:16 This is the solution we got
01:20 Check if we divided by 0
01:25 For division by 0, X must equal 6
01:28 Substitute in our equation and solve
01:34 It works out, so this is also a solution to the question
01:40 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following equation:

x2−36=6x−36 x^2-36=6x-36

2

Step-by-step solution

To solve the equation x2−36=6x−36 x^2 - 36 = 6x - 36 , follow these steps:

  • Simplify the equation by subtracting 6x and 36 from both sides to get: x2−6x=0 x^2 - 6x = 0 .
  • Notice that the equation can be factored as it has a common factor: x(x−6)=0 x(x - 6) = 0 .
  • According to the zero product property, set each factor equal to zero: x=0 x = 0 or x−6=0 x - 6 = 0 .
  • Solve each resulting equation: x=0 x = 0 and x=6 x = 6 .

Therefore, the solutions to the quadratic equation x2−36=6x−36 x^2 - 36 = 6x - 36 are x=0 x = 0 or x=6 x = 6 .

3

Final Answer

0 or 6 0~or~6

Practice Quiz

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Solve for X:

\( x\cdot x=49 \)

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