%5E2%3D44.jpeg "(4x+7)^2=44")
Solving the Equation (4x + 7)² = 44
This equation involves a squared term, which means we need to follow specific steps to solve for x.
1. Expand the Squared Term
First, expand the left side of the equation by using the FOIL method (First, Outer, Inner, Last) or by recognizing the square of a binomial pattern:
(4x + 7)² = (4x + 7)(4x + 7) = 16x² + 56x + 49
Now our equation looks like this: 16x² + 56x + 49 = 44
2. Transform into a Quadratic Equation
To solve for x, we need to transform the equation into a standard quadratic form, where one side equals zero:
16x² + 56x + 5 = 0
3. Solve the Quadratic Equation
We can solve this quadratic equation using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
Where:
- a = 16
- b = 56
- c = 5
Substitute the values into the formula and simplify:
x = (-56 ± √(56² - 4 * 16 * 5)) / (2 * 16)
x = (-56 ± √(2736)) / 32
x = (-56 ± 52.3) / 32
This gives us two possible solutions:
- x₁ = -0.115
- x₂ = -3.266
Conclusion
Therefore, the solutions for the equation (4x + 7)² = 44 are x = -0.115 and x = -3.266.