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Simplifying 10 = -5x(4x + 2) + 21x Reorder the terms: 10 = -5x(2 + 4x) + 21x 10 = (2 * -5x + 4x * -5x) + 21x 10 = (-10x + -20x2) + 21x Reorder the terms: 10 = -10x + 21x + -20x2 Combine like terms: -10x + 21x = 11x 10 = 11x + -20x2 Solving 10 = 11x + -20x2 Solving for variable 'x'. Reorder the terms: 10 + -11x + 20x2 = 11x + -11x + -20x2 + 20x2 Combine like terms: 11x + -11x = 0 10 + -11x + 20x2 = 0 + -20x2 + 20x2 10 + -11x + 20x2 = -20x2 + 20x2 Combine like terms: -20x2 + 20x2 = 0 10 + -11x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 0.5 + -0.55x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -0.55x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -0.55x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -0.55x + x2 = 0 + -0.5 -0.55x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -0.55x + x2 = -0.5 The x term is -0.55x. Take half its coefficient (-0.275). Square it (0.075625) and add it to both sides. Add '0.075625' to each side of the equation. -0.55x + 0.075625 + x2 = -0.5 + 0.075625 Reorder the terms: 0.075625 + -0.55x + x2 = -0.5 + 0.075625 Combine like terms: -0.5 + 0.075625 = -0.424375 0.075625 + -0.55x + x2 = -0.424375 Factor a perfect square on the left side: (x + -0.275)(x + -0.275) = -0.424375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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