Math  /  Algebra

QuestionSolve (x3)245=0(x-3)^{2}-45=0, where xx is a real number. Simplify your answer as much as possible. If there is more than one solution, separate them with commas If there is no solution, click "No solution."

Studdy Solution
Simplify the square root. Since 45=9×545 = 9 \times 5, we have:
45=9×5=9×5=35\sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3\sqrt{5}
Substitute back into the expression for xx:
x=3±35x = 3 \pm 3\sqrt{5}
The solutions are:
x=3+35,335 x = 3 + 3\sqrt{5}, \, 3 - 3\sqrt{5}

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