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Simplifying 6x(6x + 4) + -2(3x + 5) + 4x = 0 Reorder the terms: 6x(4 + 6x) + -2(3x + 5) + 4x = 0 (4 * 6x + 6x * 6x) + -2(3x + 5) + 4x = 0 (24x + 36x2) + -2(3x + 5) + 4x = 0 Reorder the terms: 24x + 36x2 + -2(5 + 3x) + 4x = 0 24x + 36x2 + (5 * -2 + 3x * -2) + 4x = 0 24x + 36x2 + (-10 + -6x) + 4x = 0 Reorder the terms: -10 + 24x + -6x + 4x + 36x2 = 0 Combine like terms: 24x + -6x = 18x -10 + 18x + 4x + 36x2 = 0 Combine like terms: 18x + 4x = 22x -10 + 22x + 36x2 = 0 Solving -10 + 22x + 36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 11x + 18x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 11x + 18x2)' equal to zero and attempt to solve: Simplifying -5 + 11x + 18x2 = 0 Solving -5 + 11x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.2777777778 + 0.6111111111x + x2 = 0 Move the constant term to the right: Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.6111111111x + 0.2777777778 + x2 = 0 + 0.2777777778 Reorder the terms: -0.2777777778 + 0.2777777778 + 0.6111111111x + x2 = 0 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + 0.6111111111x + x2 = 0 + 0.2777777778 0.6111111111x + x2 = 0 + 0.2777777778 Combine like terms: 0 + 0.2777777778 = 0.2777777778 0.6111111111x + x2 = 0.2777777778 The x term is 0.6111111111x. Take half its coefficient (0.3055555556). Square it (0.09336419756) and add it to both sides. Add '0.09336419756' to each side of the equation. 0.6111111111x + 0.09336419756 + x2 = 0.2777777778 + 0.09336419756 Reorder the terms: 0.09336419756 + 0.6111111111x + x2 = 0.2777777778 + 0.09336419756 Combine like terms: 0.2777777778 + 0.09336419756 = 0.37114197536 0.09336419756 + 0.6111111111x + x2 = 0.37114197536 Factor a perfect square on the left side: (x + 0.3055555556)(x + 0.3055555556) = 0.37114197536 Calculate the square root of the right side: 0.609214228 Break this problem into two subproblems by setting (x + 0.3055555556) equal to 0.609214228 and -0.609214228.Subproblem 1
x + 0.3055555556 = 0.609214228 Simplifying x + 0.3055555556 = 0.609214228 Reorder the terms: 0.3055555556 + x = 0.609214228 Solving 0.3055555556 + x = 0.609214228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3055555556' to each side of the equation. 0.3055555556 + -0.3055555556 + x = 0.609214228 + -0.3055555556 Combine like terms: 0.3055555556 + -0.3055555556 = 0.0000000000 0.0000000000 + x = 0.609214228 + -0.3055555556 x = 0.609214228 + -0.3055555556 Combine like terms: 0.609214228 + -0.3055555556 = 0.3036586724 x = 0.3036586724 Simplifying x = 0.3036586724Subproblem 2
x + 0.3055555556 = -0.609214228 Simplifying x + 0.3055555556 = -0.609214228 Reorder the terms: 0.3055555556 + x = -0.609214228 Solving 0.3055555556 + x = -0.609214228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3055555556' to each side of the equation. 0.3055555556 + -0.3055555556 + x = -0.609214228 + -0.3055555556 Combine like terms: 0.3055555556 + -0.3055555556 = 0.0000000000 0.0000000000 + x = -0.609214228 + -0.3055555556 x = -0.609214228 + -0.3055555556 Combine like terms: -0.609214228 + -0.3055555556 = -0.9147697836 x = -0.9147697836 Simplifying x = -0.9147697836Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3036586724, -0.9147697836}Solution
x = {0.3036586724, -0.9147697836}
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