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Solving the Equation (x + 7)^2 - 11 = 0
This article will walk through the steps of solving the quadratic equation (x + 7)^2 - 11 = 0.
Step 1: Isolate the Squared Term
Begin by isolating the squared term, (x + 7)^2, by adding 11 to both sides of the equation:
(x + 7)^2 = 11
Step 2: Take the Square Root of Both Sides
Next, take the square root of both sides of the equation. Remember that taking the square root of a number can result in both a positive and negative answer.
√(x + 7)^2 = ±√11
This simplifies to:
x + 7 = ±√11
Step 3: Solve for x
Finally, isolate x by subtracting 7 from both sides of the equation:
x = -7 ± √11
Solutions
Therefore, the solutions to the equation (x + 7)^2 - 11 = 0 are:
- x = -7 + √11
- x = -7 - √11
These are the exact solutions. If you want approximate decimal solutions, you can use a calculator to find the approximate values of √11 and then calculate the two values for x.