Final answer:
The given quadratic equation k² + 3k - 13 = 15 is first transformed into standard form, leading to the equation k² + 3k - 28 = 0. Using the quadratic formula with a = 1, b = 3, and c = -28, we find the solutions to be x = 4 and x = -7.
Step-by-step explanation:
The question given is a quadratic equation of the form ax² + bx + c = 0. To solve for the variable x using the quadratic formula, we first need to write the original equation, k² + 3k - 13 = 15, in standard form. This is done by moving all terms to one side of the equation resulting in k² + 3k - 28 = 0. With our constants identified as a = 1, b = 3, and c = -28, we can apply the quadratic formula x = (-b ± √(b²-4ac))/(2a).
Plugging in the values, we get:
x = (-3 ± √(3² - 4⋅(1)⋅(-28)))/(2⋅(1))
x = (-3 ± √(9+112))/(2)
x = (-3 ± √(121))/(2)
x = (-3 ± 11)/(2)
We then solve for x using the two possible values from the equation, which gives us:
x1 = (11 - 3)/2 = 4
x2 = (-11 - 3)/2 = -7
Thus, the solutions to the equation are x = 4 and x = -7.