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.

If $x = 5$ is a solution of the quadratic equation $2x^2 + (k - 1)x + 10 = 0$ , then the value of k is

Answer: $k = -11$

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 $2x^2 + (k - 1)x + 10 = 0$ . 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 $-11$ .

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If x=5x = 5x=5 is a solution of the quadratic equation 2x2+(k−1)x+10=02x^2 + (k - 1)x + 10 = 02x2+(k−1)x+10=0, then the value of k is