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Simplifying 5 = -4(3x + 1) * 13x Reorder the terms: 5 = -4(1 + 3x) * 13x Reorder the terms for easier multiplication: 5 = -4 * 13x(1 + 3x) Multiply -4 * 13 5 = -52x(1 + 3x) 5 = (1 * -52x + 3x * -52x) 5 = (-52x + -156x2) Solving 5 = -52x + -156x2 Solving for variable 'x'. Reorder the terms: 5 + 52x + 156x2 = -52x + 52x + -156x2 + 156x2 Combine like terms: -52x + 52x = 0 5 + 52x + 156x2 = 0 + -156x2 + 156x2 5 + 52x + 156x2 = -156x2 + 156x2 Combine like terms: -156x2 + 156x2 = 0 5 + 52x + 156x2 = 0 Begin completing the square. Divide all terms by 156 the coefficient of the squared term: Divide each side by '156'. 0.03205128205 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '-0.03205128205' to each side of the equation. 0.03205128205 + 0.3333333333x + -0.03205128205 + x2 = 0 + -0.03205128205 Reorder the terms: 0.03205128205 + -0.03205128205 + 0.3333333333x + x2 = 0 + -0.03205128205 Combine like terms: 0.03205128205 + -0.03205128205 = 0.00000000000 0.00000000000 + 0.3333333333x + x2 = 0 + -0.03205128205 0.3333333333x + x2 = 0 + -0.03205128205 Combine like terms: 0 + -0.03205128205 = -0.03205128205 0.3333333333x + x2 = -0.03205128205 The x term is 0.3333333333x. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333x + 0.02777777779 + x2 = -0.03205128205 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = -0.03205128205 + 0.02777777779 Combine like terms: -0.03205128205 + 0.02777777779 = -0.00427350426 0.02777777779 + 0.3333333333x + x2 = -0.00427350426 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = -0.00427350426 Can't calculate square root of the right side. The solution to this equation could not be determined.
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