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Simplifying x(15 + -3x) = 65 (15 * x + -3x * x) = 65 (15x + -3x2) = 65 Solving 15x + -3x2 = 65 Solving for variable 'x'. Reorder the terms: -65 + 15x + -3x2 = 65 + -65 Combine like terms: 65 + -65 = 0 -65 + 15x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 21.66666667 + -5x + x2 = 0 Move the constant term to the right: Add '-21.66666667' to each side of the equation. 21.66666667 + -5x + -21.66666667 + x2 = 0 + -21.66666667 Reorder the terms: 21.66666667 + -21.66666667 + -5x + x2 = 0 + -21.66666667 Combine like terms: 21.66666667 + -21.66666667 = 0.00000000 0.00000000 + -5x + x2 = 0 + -21.66666667 -5x + x2 = 0 + -21.66666667 Combine like terms: 0 + -21.66666667 = -21.66666667 -5x + x2 = -21.66666667 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -21.66666667 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -21.66666667 + 6.25 Combine like terms: -21.66666667 + 6.25 = -15.41666667 6.25 + -5x + x2 = -15.41666667 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = -15.41666667 Can't calculate square root of the right side. The solution to this equation could not be determined.
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