Question

Solve the equation by using the Quadratic Formula.

4x²+ 5x- 6= 0
If the solutions are real rational numbers, list from least to greatest, separated by a comma.
If the solutions are not real numbers, write your answer in the form a ± bi.

If the solutions are irrational, write your answer in simplified radical form, using ±
to express both solutions.

Answer 1

Answer: 4x² + 5x - 6 = 0 are x = -2 and x = 3/4.

Step-by-step explanation:

AI-generated answer

To solve the equation 4x² + 5x - 6 = 0 using the quadratic formula, we can follow these steps:

Step 1: Identify the coefficients of the equation. In this case, a = 4, b = 5, and c = -6.

Step 2: Apply the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Step 3: Substitute the values of a, b, and c into the quadratic formula:

x = (-5 ± √(5² - 4 * 4 * -6)) / (2 * 4)

Step 4: Simplify the equation inside the square root:

x = (-5 ± √(25 + 96)) / 8

x = (-5 ± √121) / 8

Step 5: Simplify the square root:

x = (-5 ± 11) / 8

Step 6: Split the equation into two separate solutions:

x₁ = (-5 + 11) / 8 = 6 / 8 = 3/4

x₂ = (-5 - 11) / 8 = -16 / 8 = -2

Step 7: List the solutions from least to greatest:

The solutions to the equation 4x² + 5x - 6 = 0 are x = -2 and x = 3/4.

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