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Simplifying -3x(6x + -1) + -2x = -7 Reorder the terms: -3x(-1 + 6x) + -2x = -7 (-1 * -3x + 6x * -3x) + -2x = -7 (3x + -18x2) + -2x = -7 Reorder the terms: 3x + -2x + -18x2 = -7 Combine like terms: 3x + -2x = 1x 1x + -18x2 = -7 Solving 1x + -18x2 = -7 Solving for variable 'x'. Reorder the terms: 7 + 1x + -18x2 = -7 + 7 Combine like terms: -7 + 7 = 0 7 + 1x + -18x2 = 0 Begin completing the square. Divide all terms by -18 the coefficient of the squared term: Divide each side by '-18'. -0.3888888889 + -0.05555555556x + x2 = 0 Move the constant term to the right: Add '0.3888888889' to each side of the equation. -0.3888888889 + -0.05555555556x + 0.3888888889 + x2 = 0 + 0.3888888889 Reorder the terms: -0.3888888889 + 0.3888888889 + -0.05555555556x + x2 = 0 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + -0.05555555556x + x2 = 0 + 0.3888888889 -0.05555555556x + x2 = 0 + 0.3888888889 Combine like terms: 0 + 0.3888888889 = 0.3888888889 -0.05555555556x + x2 = 0.3888888889 The x term is -0.05555555556x. Take half its coefficient (-0.02777777778). Square it (0.0007716049384) and add it to both sides. Add '0.0007716049384' to each side of the equation. -0.05555555556x + 0.0007716049384 + x2 = 0.3888888889 + 0.0007716049384 Reorder the terms: 0.0007716049384 + -0.05555555556x + x2 = 0.3888888889 + 0.0007716049384 Combine like terms: 0.3888888889 + 0.0007716049384 = 0.3896604938384 0.0007716049384 + -0.05555555556x + x2 = 0.3896604938384 Factor a perfect square on the left side: (x + -0.02777777778)(x + -0.02777777778) = 0.3896604938384 Calculate the square root of the right side: 0.624227918 Break this problem into two subproblems by setting (x + -0.02777777778) equal to 0.624227918 and -0.624227918.Subproblem 1
x + -0.02777777778 = 0.624227918 Simplifying x + -0.02777777778 = 0.624227918 Reorder the terms: -0.02777777778 + x = 0.624227918 Solving -0.02777777778 + x = 0.624227918 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02777777778' to each side of the equation. -0.02777777778 + 0.02777777778 + x = 0.624227918 + 0.02777777778 Combine like terms: -0.02777777778 + 0.02777777778 = 0.00000000000 0.00000000000 + x = 0.624227918 + 0.02777777778 x = 0.624227918 + 0.02777777778 Combine like terms: 0.624227918 + 0.02777777778 = 0.65200569578 x = 0.65200569578 Simplifying x = 0.65200569578Subproblem 2
x + -0.02777777778 = -0.624227918 Simplifying x + -0.02777777778 = -0.624227918 Reorder the terms: -0.02777777778 + x = -0.624227918 Solving -0.02777777778 + x = -0.624227918 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02777777778' to each side of the equation. -0.02777777778 + 0.02777777778 + x = -0.624227918 + 0.02777777778 Combine like terms: -0.02777777778 + 0.02777777778 = 0.00000000000 0.00000000000 + x = -0.624227918 + 0.02777777778 x = -0.624227918 + 0.02777777778 Combine like terms: -0.624227918 + 0.02777777778 = -0.59645014022 x = -0.59645014022 Simplifying x = -0.59645014022Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.65200569578, -0.59645014022}
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