How to solve by using the Quadratic Formula
6x2 - 7x = - 4
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3x^2 - 7x = -4
3(x^2 - 7/3 x) = -4
3(x^2 - 7/3 x + (7/6)^2) = -4 + 3(7/6)^2
3(x - 7/6)^2 = 1/12
(x - 7/6)^2 = 1/36
x - 7/6 = ±1/6
x = (7±1)/6
x = 4/3 or 1
To solve the quadratic equation 6x^2 - 7x = -4 using the Quadratic Formula, follow these steps:
Step 1: Identify the coefficients
- The quadratic equation is in the form ax^2 + bx + c = 0.
- In this case, a = 6, b = -7, and c = -4.
Step 2: Apply the Quadratic Formula
- The Quadratic Formula is x = (-b ± √(b^2 - 4ac))/(2a).
- Substitute the coefficients into the formula:
x = (-(-7) ± √((-7)^2 - 4(6)(-4))) / (2(6))
Step 3: Simplify
- Simplify the expression inside the square root:
x = (7 ± √(49 + 96)) / 12
x = (7 ± √145) / 12
Step 4: Find the two possible solutions
- Calculate both solutions by taking the positive and negative square root separately:
x1 = (7 + √145) / 12
x2 = (7 - √145) / 12
These are the two possible solutions to the quadratic equation 6x^2 - 7x = -4 when using the Quadratic Formula.