SOLUTION: I have an equation: 4x^2 - 24x + 27 = 0 The first part of the question requires me to complete the square so I get: 4*(x-3)^2 - 9 = 0 Using this, how can I solve x, WITHOUT us

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: I have an equation: 4x^2 - 24x + 27 = 0 The first part of the question requires me to complete the square so I get: 4*(x-3)^2 - 9 = 0 Using this, how can I solve x, WITHOUT us      Log On


   



Question 523334: I have an equation: 4x^2 - 24x + 27 = 0
The first part of the question requires me to complete the square so I get:
4*(x-3)^2 - 9 = 0
Using this, how can I solve x, WITHOUT using a calculator?

Found 2 solutions by gsmani_iyer, MathTherapy:
Answer by gsmani_iyer(201) About Me  (Show Source):
You can put this solution on YOUR website!
4x%5E2-24x%2B27+=+0This is to be factorized first.
4x%5E2-6x-18x%2B27+=+0
= 2x%282x-3%29-9%282x-3%29+=+0
= %282x-3%29%282x-9%29+=+0. So either of the factors is equal to 0. Because 0 multiplied by any number is equal to 0.
= If %282x-3%29+=+0, then 2x = 3; x = 3/2 = 1.5
= If %282x-9%29+=+0, then 2x = 9; x = 9/2 = 4.5
x = {1.5, 4.5} Answer.
I hope you understood this. All the best.

gsm/-

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
I have an equation: 4x^2 - 24x + 27 = 0
The first part of the question requires me to complete the square so I get:
4*(x-3)^2 - 9 = 0
Using this, how can I solve x, WITHOUT using a calculator?

4%28x+-+3%29%5E2+-+9+=+0

Add 9 to both sides of equation to get:

4%28x+-+3%29%5E2+=+9

%28x+-+3%29%5E2+=+9%2F4 ----- Dividing by 4

sqrt%28%28x+-+3%29%5E2%29 = ± sqrt%289%2F4%29 ---- Taking square root of both sides of equation

x+-+3 = ± 3%2F2

x = ± %283%2F2%29+%2B+3 ------ Adding 3 to both sides of equation

x = ± %283%2F2%29+%2B+%286%2F2%29

x = 3%2F2+%2B+6%2F2 ----- 9%2F2, or highlight_green%284.5%29

OR

x = -%283%2F2%29+%2B+6%2F2 ----- 3%2F2, or highlight_green%281.5%29

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