How do I work this correctly? I know the answer is 7 but I am doing something wrong.Here is what I have...
x+�ã(2x-5)=10
x+�ã(2x-5)^2=10^2
x+2x-5=100
3x-5+5=100+5
3x=105
x=35
PLEASE HELP!
what is the a~ all about? If it is a square root symbol then the solution looks like this:
x + (2x-5)^(1/2) = 10 : move x to other side
(2x-5)^(1/2) = 10 - x : square both sides
2x-5 = (10-x)^2 : expand the squared term
2x-5 = 100-10x-10x+x^2 : combine terms
0 = 105 - 22x + x^2 : use quadratic formula to solve for x
x =[-(-22) +/- sqrt(22^2 -4*1*105)]/(2*1)
x= [22 +/- sqrt(484 - 420)]/2
x= [22 +/- 8] / 2
x= 7 or 15
Plugging back into our initial equation shows that 7 is a solution, but 15 is not. This is because we started with a square root, which is invalid for negative numbers.
Regards.
To solve the equation correctly, you need to follow the order of operations and apply the correct rules of algebra. Let's break it down step by step:
1. Start with the original equation: x + √(2x - 5) = 10.
2. Square both sides of the equation to eliminate the square root (√): (x + √(2x - 5))^2 = 10^2.
3. Apply the square of a binomial formula: (x + √(2x - 5))^2 = 100. Expanding the left side gives x^2 + 2x√(2x - 5) + (2x - 5) = 100.
4. Simplify the equation by combining like terms: x^2 + 2x√(2x - 5) + 2x - 5 = 100.
5. Move the constant term to the right side of the equation: x^2 + 2x√(2x - 5) + 2x = 100 + 5.
6. Combine like terms: x^2 + 2x√(2x - 5) + 2x = 105.
7. Now, you have an equation that involves both the variable x and the square root term. To isolate x, you need to get rid of the square root term. One way to do this is to move the term involving the square root to the other side of the equation. Subtract 2x from both sides: x^2 + 2x√(2x - 5) = 105 - 2x.
8. Next, square both sides of the equation to eliminate the square root (√): (x^2 + 2x√(2x - 5))^2 = (105 - 2x)^2.
9. Expanding both sides gives x^4 + 4x^3√(2x - 5) + 4x^2(2x - 5) = 11025 - 420x + 4x^2.
10. Simplify further: x^4 + 4x^3√(2x - 5) + 8x^3 - 20x^2 = 11025 - 420x + 4x^2.
11. Combine like terms: x^4 + 8x^3 - 20x^2 + 4x^3√(2x - 5) - 4x^2 = 11025 - 420x.
12. Rearrange the equation: x^4 + (8x^3 + 4x^3√(2x - 5)) - (20x^2 + 4x^2) = 11025 - 420x.
13. Factor out common terms: x^4 + 12x^3 + 4x^3√(2x - 5) - 24x^2 = 11025 - 420x.
14. At this point, we can no longer proceed algebraically to solve for x. We need to apply numerical methods or approximations to find the value of x.
Based on the steps you provided, it seems like you made a mistake somewhere, resulting in the incorrect answer of x = 35. Double-check your calculations and equations to see if you made any errors.