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Simplifying 3x(6x + -1) + 2(2x + -3) = 0 Reorder the terms: 3x(-1 + 6x) + 2(2x + -3) = 0 (-1 * 3x + 6x * 3x) + 2(2x + -3) = 0 (-3x + 18x2) + 2(2x + -3) = 0 Reorder the terms: -3x + 18x2 + 2(-3 + 2x) = 0 -3x + 18x2 + (-3 * 2 + 2x * 2) = 0 -3x + 18x2 + (-6 + 4x) = 0 Reorder the terms: -6 + -3x + 4x + 18x2 = 0 Combine like terms: -3x + 4x = 1x -6 + 1x + 18x2 = 0 Solving -6 + 1x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.3333333333 + 0.05555555556x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 0.05555555556x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 0.05555555556x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 0.05555555556x + x2 = 0 + 0.3333333333 0.05555555556x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 0.05555555556x + x2 = 0.3333333333 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 = 0.3333333333 + 0.0007716049384 Reorder the terms: 0.0007716049384 + 0.05555555556x + x2 = 0.3333333333 + 0.0007716049384 Combine like terms: 0.3333333333 + 0.0007716049384 = 0.3341049382384 0.0007716049384 + 0.05555555556x + x2 = 0.3341049382384 Factor a perfect square on the left side: (x + 0.02777777778)(x + 0.02777777778) = 0.3341049382384 Calculate the square root of the right side: 0.578018112 Break this problem into two subproblems by setting (x + 0.02777777778) equal to 0.578018112 and -0.578018112.Subproblem 1
x + 0.02777777778 = 0.578018112 Simplifying x + 0.02777777778 = 0.578018112 Reorder the terms: 0.02777777778 + x = 0.578018112 Solving 0.02777777778 + x = 0.578018112 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 = 0.578018112 + -0.02777777778 Combine like terms: 0.02777777778 + -0.02777777778 = 0.00000000000 0.00000000000 + x = 0.578018112 + -0.02777777778 x = 0.578018112 + -0.02777777778 Combine like terms: 0.578018112 + -0.02777777778 = 0.55024033422 x = 0.55024033422 Simplifying x = 0.55024033422Subproblem 2
x + 0.02777777778 = -0.578018112 Simplifying x + 0.02777777778 = -0.578018112 Reorder the terms: 0.02777777778 + x = -0.578018112 Solving 0.02777777778 + x = -0.578018112 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 = -0.578018112 + -0.02777777778 Combine like terms: 0.02777777778 + -0.02777777778 = 0.00000000000 0.00000000000 + x = -0.578018112 + -0.02777777778 x = -0.578018112 + -0.02777777778 Combine like terms: -0.578018112 + -0.02777777778 = -0.60579588978 x = -0.60579588978 Simplifying x = -0.60579588978Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.55024033422, -0.60579588978}
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