SOLUTION: Please help me solve this equation 5-5 Completing the Square Solving a quadratic equation if the coefficient of x^2 is NOT 1 4x^2+24x-8=0

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Question 191078: Please help me solve this equation
5-5 Completing the Square
Solving a quadratic equation if the coefficient of x^2 is NOT 1

4x^2+24x-8=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First, let's complete the square for the left side of the equation 4x%5E2%2B24x-8=0


4x%5E2%2B24x-8 Start with the given expression.


4%28x%5E2%2B6x-2%29 Factor out the x%5E2 coefficient 4. This step is very important: the x%5E2 coefficient must be equal to 1.


Take half of the x coefficient 6 to get 3. In other words, %281%2F2%29%286%29=3.


Now square 3 to get 9. In other words, %283%29%5E2=%283%29%283%29=9


4%28x%5E2%2B6x%2Bhighlight%289-9%29-2%29 Now add and subtract 9 inside the parenthesis. Make sure to place this after the "x" term. Notice how 9-9=0. So the expression is not changed.


4%28%28x%5E2%2B6x%2B9%29-9-2%29 Group the first three terms.


4%28%28x%2B3%29%5E2-9-2%29 Factor x%5E2%2B6x%2B9 to get %28x%2B3%29%5E2.


4%28%28x%2B3%29%5E2-11%29 Combine like terms.


4%28x%2B3%29%5E2%2B4%28-11%29 Distribute.


4%28x%2B3%29%5E2-44 Multiply.


So after completing the square, 4x%5E2%2B24x-8 transforms to 4%28x%2B3%29%5E2-44. So 4x%5E2%2B24x-8=4%28x%2B3%29%5E2-44.


So 4x%5E2%2B24x-8=0 is equivalent to 4%28x%2B3%29%5E2-44=0.




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Now let's solve 4%28x%2B3%29%5E2-44=0


4%28x%2B3%29%5E2-44=0 Start with the given equation.


4%28x%2B3%29%5E2=44 Add 44 to both sides


%28x%2B3%29%5E2=%2844%29%2F%284%29 Divide both sides by 4.


%28x%2B3%29%5E2=11 Reduce.


x%2B3=%22%22%2B-sqrt%2811%29 Take the square root of both sides.


x%2B3=sqrt%2811%29 or x%2B3=-sqrt%2811%29 Break up the "plus/minus" to form two equations.


x=-3%2Bsqrt%2811%29 or x=-3-sqrt%2811%29 Subtract 3 from both sides.


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Answer:


So the solutions are x=-3%2Bsqrt%2811%29 or x=-3-sqrt%2811%29.