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Simplifying -2x(5 + 6x) = 3 + 4x (5 * -2x + 6x * -2x) = 3 + 4x (-10x + -12x2) = 3 + 4x Solving -10x + -12x2 = 3 + 4x Solving for variable 'x'. Reorder the terms: -3 + -10x + -4x + -12x2 = 3 + 4x + -3 + -4x Combine like terms: -10x + -4x = -14x -3 + -14x + -12x2 = 3 + 4x + -3 + -4x Reorder the terms: -3 + -14x + -12x2 = 3 + -3 + 4x + -4x Combine like terms: 3 + -3 = 0 -3 + -14x + -12x2 = 0 + 4x + -4x -3 + -14x + -12x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -3 + -14x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(3 + 14x + 12x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + 14x + 12x2)' equal to zero and attempt to solve: Simplifying 3 + 14x + 12x2 = 0 Solving 3 + 14x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.25 + 1.166666667x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 1.166666667x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 1.166666667x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 1.166666667x + x2 = 0 + -0.25 1.166666667x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 1.166666667x + x2 = -0.25 The x term is 1.166666667x. Take half its coefficient (0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. 1.166666667x + 0.3402777780 + x2 = -0.25 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667x + x2 = -0.25 + 0.3402777780 Combine like terms: -0.25 + 0.3402777780 = 0.090277778 0.3402777780 + 1.166666667x + x2 = 0.090277778 Factor a perfect square on the left side: (x + 0.5833333335)(x + 0.5833333335) = 0.090277778 Calculate the square root of the right side: 0.300462607 Break this problem into two subproblems by setting (x + 0.5833333335) equal to 0.300462607 and -0.300462607.Subproblem 1
x + 0.5833333335 = 0.300462607 Simplifying x + 0.5833333335 = 0.300462607 Reorder the terms: 0.5833333335 + x = 0.300462607 Solving 0.5833333335 + x = 0.300462607 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + x = 0.300462607 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = 0.300462607 + -0.5833333335 x = 0.300462607 + -0.5833333335 Combine like terms: 0.300462607 + -0.5833333335 = -0.2828707265 x = -0.2828707265 Simplifying x = -0.2828707265Subproblem 2
x + 0.5833333335 = -0.300462607 Simplifying x + 0.5833333335 = -0.300462607 Reorder the terms: 0.5833333335 + x = -0.300462607 Solving 0.5833333335 + x = -0.300462607 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + x = -0.300462607 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = -0.300462607 + -0.5833333335 x = -0.300462607 + -0.5833333335 Combine like terms: -0.300462607 + -0.5833333335 = -0.8837959405 x = -0.8837959405 Simplifying x = -0.8837959405Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.2828707265, -0.8837959405}Solution
x = {-0.2828707265, -0.8837959405}
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