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Simplifying -12x2 = 3x + -28 Reorder the terms: -12x2 = -28 + 3x Solving -12x2 = -28 + 3x Solving for variable 'x'. Reorder the terms: 28 + -3x + -12x2 = -28 + 3x + 28 + -3x Reorder the terms: 28 + -3x + -12x2 = -28 + 28 + 3x + -3x Combine like terms: -28 + 28 = 0 28 + -3x + -12x2 = 0 + 3x + -3x 28 + -3x + -12x2 = 3x + -3x Combine like terms: 3x + -3x = 0 28 + -3x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -2.333333333 + 0.25x + x2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + 0.25x + 2.333333333 + x2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + 0.25x + x2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + 0.25x + x2 = 0 + 2.333333333 0.25x + x2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 0.25x + x2 = 2.333333333 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 = 2.333333333 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 2.333333333 + 0.015625 Combine like terms: 2.333333333 + 0.015625 = 2.348958333 0.015625 + 0.25x + x2 = 2.348958333 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 2.348958333 Calculate the square root of the right side: 1.53263118 Break this problem into two subproblems by setting (x + 0.125) equal to 1.53263118 and -1.53263118.Subproblem 1
x + 0.125 = 1.53263118 Simplifying x + 0.125 = 1.53263118 Reorder the terms: 0.125 + x = 1.53263118 Solving 0.125 + x = 1.53263118 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 = 1.53263118 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 1.53263118 + -0.125 x = 1.53263118 + -0.125 Combine like terms: 1.53263118 + -0.125 = 1.40763118 x = 1.40763118 Simplifying x = 1.40763118Subproblem 2
x + 0.125 = -1.53263118 Simplifying x + 0.125 = -1.53263118 Reorder the terms: 0.125 + x = -1.53263118 Solving 0.125 + x = -1.53263118 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 = -1.53263118 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -1.53263118 + -0.125 x = -1.53263118 + -0.125 Combine like terms: -1.53263118 + -0.125 = -1.65763118 x = -1.65763118 Simplifying x = -1.65763118Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.40763118, -1.65763118}
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