(x%2B1)%3D26.jpeg "(6x+7)(x+1)=26")
Solving the Equation (6x + 7)(x + 1) = 26
This article will guide you through the process of solving the quadratic equation (6x + 7)(x + 1) = 26.
Step 1: Expand the Left Side
First, we need to expand the left side of the equation by multiplying the two binomials:
(6x + 7)(x + 1) = 6x² + 6x + 7x + 7
Simplifying the expression, we get:
6x² + 13x + 7 = 26
Step 2: Move All Terms to One Side
Now, we need to move all terms to one side of the equation to get a standard quadratic form:
6x² + 13x + 7 - 26 = 0
Simplifying the expression:
6x² + 13x - 19 = 0
Step 3: Solve the Quadratic Equation
We can solve the quadratic equation using different methods like factoring, completing the square, or the quadratic formula. In this case, factoring might be a bit challenging. Let's use the quadratic formula:
x = [-b ± √(b² - 4ac)] / 2a
Where a = 6, b = 13, and c = -19.
Plugging in the values:
x = [-13 ± √(13² - 4 * 6 * -19)] / (2 * 6)
x = [-13 ± √(169 + 456)] / 12
x = [-13 ± √(625)] / 12
x = [-13 ± 25] / 12
This gives us two possible solutions:
x1 = (-13 + 25) / 12 = 1
x2 = (-13 - 25) / 12 = -3
Conclusion
Therefore, the solutions to the equation (6x + 7)(x + 1) = 26 are x = 1 and x = -3.