x^2+(x-2)^2 = (2x-6)^2
solve for x.
thanks so much.
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it was a word problem and i already got it into an equation. i tried solving it but having a hard time on where to start to solve for x. Thanks.
Try expanding the part you have in parentheses (use the FOIL method), then combine like terms and work with what's left.
this was what i got.
-2x^2-40
possible to factor? how? please help.
You can factor a two out. However, I didn't get that set of values when I expanded and combined the terms from the original set up you posted.
Like in case of the other problem, if you plan to solve the quadratic using trial and error (using sum and product of roots), then you could try to find one or both roots by inspection or other manipulations that require less work than expanding out the quadratic and writing it in standard form first.
x^2+(x-2)^2 = (2x-6)^2
You don't have to look at this long to see that x = 2 is a solution. To find the other solution, let's write the equation as:
x^2 - (2x-6)^2 = -(x-2)^2
And use the formula
A^2 - B^2 = (A+B)(A-B)
[x + (2x-6)][x - (2x-6)] = -(x-2)^2 --->
(3x - 6)(x+6) = (x-2)^2
We can write 3x-6 = 3(x-2). If we divide both sides by x - 2 we can find the oher solution:
3x + 18 = x - 2 --->
x = 8
Correction (a few sign errors):
And use the formula
A^2 - B^2 = (A+B)(A-B)
[x + (2x-6)][x - (2x-6)] = -(x-2)^2 --->
(3x - 6)(x-6) = (x-2)^2
We can write 3x-6 = 3(x-2). If we divide both sides by x - 2 we can find the other solution:
3x - 18 = x - 2 --->
x = 8
To solve the equation x^2 + (x-2)^2 = (2x-6)^2, follow these steps:
1. Expand the terms in parentheses:
x^2 + (x-2)(x-2) = (2x-6)(2x-6)
2. Simplify each side of the equation:
x^2 + (x^2 - 4x + 4) = (4x^2 - 24x + 36)
3. Combine like terms:
2x^2 - 4x + 4 = 4x^2 - 24x + 36
4. Move all terms to one side of the equation to set it equal to zero:
0 = 2x^2 - 4x + 4 - 4x^2 + 24x - 36
5. Simplify further:
0 = -2x^2 + 20x - 32
6. To solve this quadratic equation, you can either factor it or use the quadratic formula. Let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For this equation, a = -2, b = 20, and c = -32.
7. Substitute these values into the quadratic formula and simplify:
x = (-20 ± √(20^2 - 4(-2)(-32))) / (2(-2))
x = (-20 ± √(400 - 256)) / (-4)
x = (-20 ± √144) / (-4)
x = (-20 ± 12) / (-4)
8. Simplify further:
x = (-20 + 12) / (-4) or x = (-20 - 12) / (-4)
x = -8 / -4 or x = -32 / -4
x = 2 or x = 8
So the solutions to the equation are x = 2 and x = 8.
To solve the equation x^2 + (x-2)^2 = (2x-6)^2, we can start by expanding the terms using the FOIL method.
(x-2)^2 equals (x-2)(x-2), which can be expanded as x^2 - 4x + 4.
(2x-6)^2 equals (2x-6)(2x-6), which can be expanded as 4x^2 - 24x + 36.
Now, we can substitute these expansions into the original equation and simplify:
x^2 + (x-2)^2 = (2x-6)^2
x^2 + (x^2 - 4x + 4) = (4x^2 - 24x + 36)
Combine like terms:
2x^2 - 4x + 4 = 4x^2 - 24x + 36
To solve for x, we can bring all the terms to one side and set the equation equal to zero:
0 = 4x^2 - 2x^2 - 24x + 4x - 36 + 4
Combine like terms again:
0 = 2x^2 - 20x - 32
To see if this quadratic equation can be factored, we can look for factors of -32 that add up to -20. After some inspection, we find that -4 and 8 are the appropriate factors:
0 = (2x - 4)(x + 8)
Now we can set each factor equal to zero and solve for x:
2x - 4 = 0 gives x = 2
x + 8 = 0 gives x = -8
So the solution to the equation x^2 + (x-2)^2 = (2x-6)^2 is x = 2 and x = -8.