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Simplifying 2x(4x + -12) = 3 Reorder the terms: 2x(-12 + 4x) = 3 (-12 * 2x + 4x * 2x) = 3 (-24x + 8x2) = 3 Solving -24x + 8x2 = 3 Solving for variable 'x'. Reorder the terms: -3 + -24x + 8x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -24x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.375 + -3x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -3x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -3x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -3x + x2 = 0 + 0.375 -3x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -3x + x2 = 0.375 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 0.375 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 0.375 + 2.25 Combine like terms: 0.375 + 2.25 = 2.625 2.25 + -3x + x2 = 2.625 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 2.625 Calculate the square root of the right side: 1.620185175 Break this problem into two subproblems by setting (x + -1.5) equal to 1.620185175 and -1.620185175.Subproblem 1
x + -1.5 = 1.620185175 Simplifying x + -1.5 = 1.620185175 Reorder the terms: -1.5 + x = 1.620185175 Solving -1.5 + x = 1.620185175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.620185175 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.620185175 + 1.5 x = 1.620185175 + 1.5 Combine like terms: 1.620185175 + 1.5 = 3.120185175 x = 3.120185175 Simplifying x = 3.120185175Subproblem 2
x + -1.5 = -1.620185175 Simplifying x + -1.5 = -1.620185175 Reorder the terms: -1.5 + x = -1.620185175 Solving -1.5 + x = -1.620185175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.620185175 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.620185175 + 1.5 x = -1.620185175 + 1.5 Combine like terms: -1.620185175 + 1.5 = -0.120185175 x = -0.120185175 Simplifying x = -0.120185175Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.120185175, -0.120185175}
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