%5E2%3D9.jpeg "(4x+5)^2=9")
Solving the Equation (4x + 5)² = 9
This article will guide you through the steps to solve the equation (4x + 5)² = 9.
Understanding the Equation
The equation involves a squared term, (4x + 5)², which means we need to find the value of 'x' that satisfies the equation.
Solving for 'x'
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Take the square root of both sides:
√((4x + 5)²) = ±√9
This gives us two possible equations:
- 4x + 5 = 3
- 4x + 5 = -3
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Solve for 'x' in each equation:
Equation 1: 4x + 5 = 3
- Subtract 5 from both sides: 4x = -2
- Divide both sides by 4: x = -1/2
Equation 2: 4x + 5 = -3
- Subtract 5 from both sides: 4x = -8
- Divide both sides by 4: x = -2
The Solutions
Therefore, the solutions to the equation (4x + 5)² = 9 are x = -1/2 and x = -2.
Verifying the Solutions
We can verify our solutions by plugging them back into the original equation:
- For x = -1/2: (4 * (-1/2) + 5)² = (3)² = 9
- For x = -2: (4 * (-2) + 5)² = (-3)² = 9
Both solutions satisfy the original equation, confirming their correctness.