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Simplifying 12x2 = 13 + -3x Solving 12x2 = 13 + -3x Solving for variable 'x'. Reorder the terms: -13 + 3x + 12x2 = 13 + -3x + -13 + 3x Reorder the terms: -13 + 3x + 12x2 = 13 + -13 + -3x + 3x Combine like terms: 13 + -13 = 0 -13 + 3x + 12x2 = 0 + -3x + 3x -13 + 3x + 12x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -13 + 3x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -1.083333333 + 0.25x + x2 = 0 Move the constant term to the right: Add '1.083333333' to each side of the equation. -1.083333333 + 0.25x + 1.083333333 + x2 = 0 + 1.083333333 Reorder the terms: -1.083333333 + 1.083333333 + 0.25x + x2 = 0 + 1.083333333 Combine like terms: -1.083333333 + 1.083333333 = 0.000000000 0.000000000 + 0.25x + x2 = 0 + 1.083333333 0.25x + x2 = 0 + 1.083333333 Combine like terms: 0 + 1.083333333 = 1.083333333 0.25x + x2 = 1.083333333 The x term is 0.25x. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25x + 0.015625 + x2 = 1.083333333 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 1.083333333 + 0.015625 Combine like terms: 1.083333333 + 0.015625 = 1.098958333 0.015625 + 0.25x + x2 = 1.098958333 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 1.098958333 Calculate the square root of the right side: 1.048312135 Break this problem into two subproblems by setting (x + 0.125) equal to 1.048312135 and -1.048312135.Subproblem 1
x + 0.125 = 1.048312135 Simplifying x + 0.125 = 1.048312135 Reorder the terms: 0.125 + x = 1.048312135 Solving 0.125 + x = 1.048312135 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = 1.048312135 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 1.048312135 + -0.125 x = 1.048312135 + -0.125 Combine like terms: 1.048312135 + -0.125 = 0.923312135 x = 0.923312135 Simplifying x = 0.923312135Subproblem 2
x + 0.125 = -1.048312135 Simplifying x + 0.125 = -1.048312135 Reorder the terms: 0.125 + x = -1.048312135 Solving 0.125 + x = -1.048312135 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = -1.048312135 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -1.048312135 + -0.125 x = -1.048312135 + -0.125 Combine like terms: -1.048312135 + -0.125 = -1.173312135 x = -1.173312135 Simplifying x = -1.173312135Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.923312135, -1.173312135}
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