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The square of a number added to 25 equals 10 times the number. What is the number?
Let x = the number. The statement, "The square of a number added to 25 equals 10 times the number," translates to the equation x2 + 25 = 10x. Put the equation in standard form ax2 + bx + c 0, and set it equal to zero: x2 - 10x + 25 = 0. Factor the left side of the equation: (x - 5)(x - 5) = 0. Set each factor equal to zero and solve: x - 5 = 0 or x - 5 = 0; x = 5 or x = 5. The number is 5.
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