(6x-1)%3D120.jpeg "(2x+5)(6x-1)=120")
Solving the Equation (2x + 5)(6x - 1) = 120
This article will guide you through the steps of solving the equation (2x + 5)(6x - 1) = 120.
1. Expand the Equation
First, we need to expand the left side of the equation by multiplying the two binomials:
(2x + 5)(6x - 1) = 12x² - 2x + 30x - 5
Simplifying the expression, we get:
12x² + 28x - 5 = 120
2. Move all Terms to One Side
To solve the quadratic equation, we need to set it equal to zero. Subtract 120 from both sides:
12x² + 28x - 125 = 0
3. Solve the Quadratic Equation
Now we have a standard quadratic equation in the form ax² + bx + c = 0. There are a few methods to solve this:
- Factoring: Try to factor the quadratic expression into two binomials. In this case, factoring might be a bit tricky.
- Quadratic Formula: The most reliable method for solving quadratic equations is the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
Where a = 12, b = 28, and c = -125.
Substituting the values into the formula and simplifying, we obtain the solutions:
x = (-28 ± √(28² - 4 * 12 * -125)) / (2 * 12)
x = (-28 ± √(6884)) / 24
x = (-28 ± 83) / 24
This gives us two possible solutions:
- x = (55 / 24)
- x = (-111 / 24)
4. Verify the Solutions
It's always a good idea to plug your solutions back into the original equation to verify they are correct. In this case, both solutions should work.
Conclusion
By following the steps above, we successfully solved the equation (2x + 5)(6x - 1) = 120, finding two solutions for x: (55/24) and (-111/24).