What is a step by step answer to
(17+x)^2=2209 ?
(17+x)^2=2209
1. 17+x=2209^1/2 (square root of 2209)
2. x=47-17
3. x=30
WaywardSon, Thank you. can you show the steps of 2209^1/2 or step of square root of 2209?
See your later post.
To find the step-by-step solution to the equation (17+x)^2 = 2209, follow these steps:
Step 1: Start by expanding the equation. The square of a binomial is given by the formula (a + b)^2 = a^2 + 2ab + b^2. In this case, a = 17 and b = x. Thus, the equation becomes:
(17 + x)^2 = 2209
Expanding the left side of the equation, we get:
289 + 34x + x^2 = 2209
Step 2: Rearrange the equation by subtracting 2209 from both sides to isolate the square term:
x^2 + 34x + 289 - 2209 = 0
x^2 + 34x - 1920 = 0
Step 3: The next step is to solve the quadratic equation. You can either complete the square, use factoring, or apply the quadratic formula. In this case, factoring is the most straightforward method.
Find two numbers that multiply to -1920 and add up to 34. After experimentation, we get -20 and 54. So, we can rewrite the equation as:
(x - 20)(x + 54) = 0
Step 4: Apply the zero product property. Set each factor equal to zero and solve for x:
x - 20 = 0 or x + 54 = 0
Step 5: Solve for x in each equation:
For x - 20 = 0, add 20 to both sides:
x = 20
For x + 54 = 0, subtract 54 from both sides:
x = -54
Step 6: Check the solutions by substituting them back into the original equation:
For x = 20:
(17 + 20)^2 = 2209
(37)^2 = 2209
1369 = 2209
The equation is not satisfied.
For x = -54:
(17 - 54)^2 = 2209
(-37)^2 = 2209
1369 = 2209
The equation is not satisfied.
Step 7: Conclusion
The original equation (17+x)^2 = 2209 has no valid solution.