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Q. Solve by completing the square.Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth._____ or _____
- Rewrite in standard form: Rewrite the equation in the form of .Add to both sides to set the equation up for completing the square.
- Complete the square: Choose the number to add to both sides to complete the square.Since , add to both sides.
- Factor left side: Identify the equation after factoring the left side.
- Take square root: Identify the equation after taking the square root on both sides.Take the square root of both sides of the equation.\$\sqrt{(z + 4)^2} = \sqrt{49}\)\(\newline\)\(z + 4 = \pm\sqrt{49}\)\(\newline\)\(z + 4 = \pm7\)
- Isolate variable: We found:\(\newline\)\(z + 4 = \pm7\)\(\newline\)Choose the equation after isolating the variable \(z\).\(\newline\)To isolate \(z\), subtract \(4\) from both sides of the equation.\(\newline\)\(z + 4 - 4 = \pm7 - 4\)\(\newline\)\(z = -4 \pm 7\)
- Find values of z: We have:\(\newline\)\(z = -4 \pm 7\)\(\newline\)What are the two values of \(z\)?\(\newline\)\(z = -4 + 7\) implies \(z = 3\).\(\newline\)\(z = -4 - 7\) implies \(z = -11\).\(\newline\)Values of \(z\): \(3\), \(-11\)
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