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Simplifying 5 = -3(2x + 1) * 7x Reorder the terms: 5 = -3(1 + 2x) * 7x Reorder the terms for easier multiplication: 5 = -3 * 7x(1 + 2x) Multiply -3 * 7 5 = -21x(1 + 2x) 5 = (1 * -21x + 2x * -21x) 5 = (-21x + -42x2) Solving 5 = -21x + -42x2 Solving for variable 'x'. Reorder the terms: 5 + 21x + 42x2 = -21x + 21x + -42x2 + 42x2 Combine like terms: -21x + 21x = 0 5 + 21x + 42x2 = 0 + -42x2 + 42x2 5 + 21x + 42x2 = -42x2 + 42x2 Combine like terms: -42x2 + 42x2 = 0 5 + 21x + 42x2 = 0 Begin completing the square. Divide all terms by 42 the coefficient of the squared term: Divide each side by '42'. 0.119047619 + 0.5x + x2 = 0 Move the constant term to the right: Add '-0.119047619' to each side of the equation. 0.119047619 + 0.5x + -0.119047619 + x2 = 0 + -0.119047619 Reorder the terms: 0.119047619 + -0.119047619 + 0.5x + x2 = 0 + -0.119047619 Combine like terms: 0.119047619 + -0.119047619 = 0.000000000 0.000000000 + 0.5x + x2 = 0 + -0.119047619 0.5x + x2 = 0 + -0.119047619 Combine like terms: 0 + -0.119047619 = -0.119047619 0.5x + x2 = -0.119047619 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = -0.119047619 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = -0.119047619 + 0.0625 Combine like terms: -0.119047619 + 0.0625 = -0.056547619 0.0625 + 0.5x + x2 = -0.056547619 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = -0.056547619 Can't calculate square root of the right side. The solution to this equation could not be determined.
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