Final answer:
To find the value of k that will make the coefficient of x^2 equal to 15, set the coefficient of x^2 in the difference expression equal to 15 and solve for k using the quadratic formula.
Step-by-step explanation:
To find the value of k that will make the coefficient of x2 equal to 15, we need to set the coefficient of x2 in the difference expression equal to 15 and solve for k. So, we have:
(9x2 - 6x + 7) - (kx2 + 4x - 12) = 15
Expanding and simplifying the expression, we get:
(9 - k)x2 + (-6 - 4)x + (7 + 12 - 15) = 0
Comparing the equation with the general quadratic equation ax2 + bx + c = 0, we have a = 9 - k, b = -6 - 4, and c = 7 + 12 - 15. Since we want the coefficient of x2 to be 15, we set a = 15. Substituting the values, we have:
15x2 + (-10)x - 4 = 0
Now we can use the quadratic formula to solve for x and find the value of k.