If x=5 is a solution of the quadratic equation 2x2+(k−1)x+10=0, then the value of k is
Get the complete, step-by-step math solution for: "If x = 5 is a solution of the quadratic equation 2x² + (k - 1)x + 10 = 0, then the value of k is". Powered by SolveForX AI math tutor.
Step-by-Step Solution
Step 1: Substitute the given solution into the equation
Since x=5 is a solution to the quadratic equation, we can substitute x=5 into the equation 2x2+(k−1)x+10=0. This will allow us to form an equation solely in terms of k.
Step 2: Simplify the equation
First, calculate the square of 5, which is 25. Then, distribute the 5 into the term (k−1) to get 5k−5. Finally, combine all the constant terms.
Step 3: Combine constant terms
Add the constant terms together: 50−5+10=45+10=55. This simplifies the equation to 5k+55=0.
Step 4: Isolate k
To isolate k, first subtract 55 from both sides of the equation. Then, divide both sides by 5 to find the value of k.
Step 5: Calculate the value of k
Performing the division, −55 divided by 5 gives −11. Therefore, the value of k is −11.