Final answer:
To solve the quadratic equation x^2 = 5x + 14 using the quadratic formula, rearrange it to x^2 - 5x - 14 = 0 and plug the coefficients into the formula. The solutions are x = 7 and x = -2.
Step-by-step explanation:
How to Solve the Quadratic Equation Using the Quadratic Formula
The student is asked to solve the equation x^2 = 5x + 14 using the quadratic formula. First, we need to rearrange the equation so that it is in standard quadratic form ax^2 + bx + c = 0. Subtracting 5x and 14 from both sides gives us x^2 - 5x - 14 = 0. Now, we can apply the quadratic formula, which is x = (-b ± √(b^2 - 4ac)) / (2a), where a = 1, b = -5, and c = -14.
Plugging the values into the formula gives us two possible solutions for x:
- x = (5 ± √((5)^2 - 4(1)(-14)))/(2(1))
- x = (5 ± √(25 + 56))/(2)
- x = (5 ± √81)/(2)
- x = (5 ± 9)/(2)
Therefore, the solutions are x = (5 + 9)/2 = 7 and x = (5 - 9)/2 = -2.