SOLUTION: 1 Solve by completing the square X^2 + 10x +13 = 0 2. Solve using the quadratic formula X^2 - 2x = 5x-2 3. Solve using quadratic formula x^2 - 3x - 3 = -5

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: 1 Solve by completing the square X^2 + 10x +13 = 0 2. Solve using the quadratic formula X^2 - 2x = 5x-2 3. Solve using quadratic formula x^2 - 3x - 3 = -5      Log On


   

Question 157979: 1 Solve by completing the square
X^2 + 10x +13 = 0
2. Solve using the quadratic formula
X^2 - 2x = 5x-2
3. Solve using quadratic formula
x^2 - 3x - 3 = -5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first two to get you started


# 1



x%5E2%2B10x%2B13 Start with the given expression.


Take half of the x coefficient 10 to get 5. In other words, %281%2F2%29%2810%29=5.


Now square 5 to get 25. In other words, %285%29%5E2=%285%29%285%29=25


x%5E2%2B10x%2Bhighlight%2825-25%29%2B13 Now add and subtract 25. Make sure to place this after the "x" term. Notice how 25-25=0. So the expression is not changed.


%28x%5E2%2B10x%2B25%29-25%2B13 Group the first three terms.


%28x%2B5%29%5E2-25%2B13 Factor x%5E2%2B10x%2B25 to get %28x%2B5%29%5E2.


%28x%2B5%29%5E2-12 Combine like terms.


So after completing the square, x%5E2%2B10x%2B13 transforms to %28x%2B5%29%5E2-12. So x%5E2%2B10x%2B13=%28x%2B5%29%5E2-12.


So x%5E2%2B10x%2B13=0 is equivalent to %28x%2B5%29%5E2-12=0.


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%28x%2B5%29%5E2-12=0 Start with the given equation.


%28x%2B5%29%5E2=0%2B12Add 12 to both sides.


%28x%2B5%29%5E2=12 Combine like terms.


x%2B5=0%2B-sqrt%2812%29 Take the square root of both sides.


x%2B5=sqrt%2812%29 or x%2B5=-sqrt%2812%29 Break up the "plus/minus" to form two equations.


x%2B5=2%2Asqrt%283%29 or x%2B5=-2%2Asqrt%283%29 Simplify the square root.


x=-5%2B2%2Asqrt%283%29 or x=-5-2%2Asqrt%283%29 Subtract 5 from both sides.


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Answer:


So the solutions are x=-5%2B2%2Asqrt%283%29 or x=-5-2%2Asqrt%283%29.






# 2



x%5E2-2x=5x-2 Start with the given equation.


x%5E2-2x-5x%2B2=0 Subtract 5x from both sides. Add 2 to both sides.


x%5E2-7x%2B2=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-7, and c=2


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%28-7%29+%2B-+sqrt%28+%28-7%29%5E2-4%281%29%282%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-7, and c=2


x+=+%287+%2B-+sqrt%28+%28-7%29%5E2-4%281%29%282%29+%29%29%2F%282%281%29%29 Negate -7 to get 7.


x+=+%287+%2B-+sqrt%28+49-4%281%29%282%29+%29%29%2F%282%281%29%29 Square -7 to get 49.


x+=+%287+%2B-+sqrt%28+49-8+%29%29%2F%282%281%29%29 Multiply 4%281%29%282%29 to get 8


x+=+%287+%2B-+sqrt%28+41+%29%29%2F%282%281%29%29 Subtract 8 from 49 to get 41


x+=+%287+%2B-+sqrt%28+41+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%287%2Bsqrt%2841%29%29%2F%282%29 or x+=+%287-sqrt%2841%29%29%2F%282%29 Break up the expression.


So the answers are x+=+%287%2Bsqrt%2841%29%29%2F%282%29 or x+=+%287-sqrt%2841%29%29%2F%282%29


which approximate to x=6.702 or x=0.298