Question

Consider this quadratic equation.

x + 3 = 4x
Which expression correctly sets up the quadratic formula to solve the equation?

Option 1: -(-4) + (-4) - 4(1)(3) / 2(1)
Option 2: -(-4) + √(-3)² - 4(1)(4) / 2(1)
Option 3: -(-4) + 4² - (1)(3) / 2(1)
Option 4: -4 = 4² - 4(1)(3) / 2(1)

Answer 1

The quadratic equation x + 3 = 4x is actually linear after rearranging it to 0 = 3x - 3. However, if the intended equation was quadratic, x^2 + 3 = 4x, the correct setup using the quadratic formula is -(-4) ± √((-4)^2 - 4(1)(3)) / (2(1)), though none of the options provided are completely correct.

Step-by-step explanation:

The quadratic equation in question is x + 3 = 4x. To solve this, we first need to rearrange the equation to get it into the standard quadratic form of ax^2 + bx + c = 0. Subtracting x from both sides, the equation becomes 0 = 3x - 3. This, however, is not a quadratic equation but a linear one, and it looks like there might be a mistake in the original equation or in the options provided.

If we consider that the equation might have meant to be x^2 + 3 = 4x, we would rearrange it as x^2 - 4x + 3 = 0. In this case, the quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a), where a = 1, b = -4, and c = 3. Plugging these values into the formula, none of the provided options correctly represent the quadratic formula setup for this equation.For the corrected equation x^2 - 4x + 3 = 0, the correct setup would be Option 2: -(-4) ± √((-4)^2 - 4(1)(3)) / (2(1)), assuming the typo in the original question is amended to include the ± symbol, indicating both the possible positive and negative square root outcomes.