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the difference between two times the square of a number and five times the number is 75.
Look at the red words:
the difference between two times the square of a number and five times the number is 75.
Replace each by x.
the difference between two times the square of x and five times x is 75.
Look at the blue words:
the difference between two times the square of x and five times x is 75.
Replace them by x²
the difference between two times x² and five times x is 75.
Look at the red words:
the difference between two times x² and five times x is 75.
Replace them by 5x
the difference between two times x² and 5x is 75
Look at the blue words:
the difference between two times x² and 5x is 75.
Replace them by 2x²
the difference between 2x² and 5x is 75.
Look at the red words:
the difference between 2x² and 5x is 75.
Replace them by the subtraction of the first minus the second,
or 2x² - 5x
2x² - 5x is 75.
Look at the blue word:
2x² - 5x is 75.
Replace it by an equal sign " = ":
2x² - 5x = 75.
Solve that:
2x² - 5x - 75 = 0
Factoring:
(2x - 15)(x + 5) = 0
2x - 15 = 0 gives solution x = 
x + 5 = 0 gives solution x = -5
Edwin
