Final answer:
To find the simplest form of the quadratic equation x² + 29 = 4x, we can rearrange it into standard form and use the quadratic formula. The solutions are x ≈ -1.65 and x ≈ 5.65.
Step-by-step explanation:
We can solve this quadratic equation by rearranging it into standard form, which is ax² + bx + c = 0. In this case, the equation is x² + 29 = 4x. Subtracting 4x from both sides gives us x² - 4x + 29 = 0. Now, we can use the quadratic formula, which states that the solutions to the equation ax² + bx + c = 0 are given by:
x = (-b ± √(b² - 4ac)) / (2a)
For our equation, a = 1, b = -4, and c = 29. Plugging these values into the formula, we get:
x = (-(-4) ± √((-4)² - 4(1)(29))) / (2(1))
Calculating this expression gives us two solutions: x ≈ -1.65 and x ≈ 5.65. Therefore, the simplest form of the quadratic equation x² + 29 = 4x is x ≈ -1.65 and x ≈ 5.65.