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Simplifying 4x + -3 + 12x2 = 0 Reorder the terms: -3 + 4x + 12x2 = 0 Solving -3 + 4x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.25 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 0.3333333333x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 0.3333333333x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 0.3333333333x + x2 = 0 + 0.25 0.3333333333x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 0.3333333333x + x2 = 0.25 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 = 0.25 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = 0.25 + 0.02777777779 Combine like terms: 0.25 + 0.02777777779 = 0.27777777779 0.02777777779 + 0.3333333333x + x2 = 0.27777777779 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 0.27777777779 Calculate the square root of the right side: 0.527046277 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 0.527046277 and -0.527046277.Subproblem 1
x + 0.1666666667 = 0.527046277 Simplifying x + 0.1666666667 = 0.527046277 Reorder the terms: 0.1666666667 + x = 0.527046277 Solving 0.1666666667 + x = 0.527046277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = 0.527046277 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 0.527046277 + -0.1666666667 x = 0.527046277 + -0.1666666667 Combine like terms: 0.527046277 + -0.1666666667 = 0.3603796103 x = 0.3603796103 Simplifying x = 0.3603796103Subproblem 2
x + 0.1666666667 = -0.527046277 Simplifying x + 0.1666666667 = -0.527046277 Reorder the terms: 0.1666666667 + x = -0.527046277 Solving 0.1666666667 + x = -0.527046277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = -0.527046277 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -0.527046277 + -0.1666666667 x = -0.527046277 + -0.1666666667 Combine like terms: -0.527046277 + -0.1666666667 = -0.6937129437 x = -0.6937129437 Simplifying x = -0.6937129437Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3603796103, -0.6937129437}
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