Final answer:
To solve the quadratic equation x^2 - 7x = -13, bring all terms to one side, apply the quadratic formula, and find that there are no real solutions since the discriminant (b^2 - 4ac) is negative.
Step-by-step explanation:
Solving the Quadratic Equation
To solve the quadratic equation x^2 - 7x = -13, we first bring all terms to one side to set the equation to zero: x^2 - 7x + 13 = 0. This is in the standard form of a quadratic equation, which is ax^2 + bx + c = 0, where in this case, a=1, b=-7, and c=13.
We can then apply the quadratic formula, which is x = (-b ± √(b^2 - 4ac)) / (2a). Substituting our values into the formula, we get:
x = (7 ± √((-7)^2 - 4(1)(13))) / (2(1))
x = (7 ± √(49 - 52)) / 2
However, since 49 - 52 results in a negative number, we find that there are no real solutions to this equation because the square root of a negative number is not a real number. Instead, the equation has two complex solutions which are not covered in this solution process.