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Simplifying 1x + 2(4 + 2x) + -1(3 + 2x) + 4 = 3(2 + 1x) * 3x + 2(4 + 1x) + -2 1x + (4 * 2 + 2x * 2) + -1(3 + 2x) + 4 = 3(2 + 1x) * 3x + 2(4 + 1x) + -2 1x + (8 + 4x) + -1(3 + 2x) + 4 = 3(2 + 1x) * 3x + 2(4 + 1x) + -2 1x + 8 + 4x + (3 * -1 + 2x * -1) + 4 = 3(2 + 1x) * 3x + 2(4 + 1x) + -2 1x + 8 + 4x + (-3 + -2x) + 4 = 3(2 + 1x) * 3x + 2(4 + 1x) + -2 Reorder the terms: 8 + -3 + 4 + 1x + 4x + -2x = 3(2 + 1x) * 3x + 2(4 + 1x) + -2 Combine like terms: 8 + -3 = 5 5 + 4 + 1x + 4x + -2x = 3(2 + 1x) * 3x + 2(4 + 1x) + -2 Combine like terms: 5 + 4 = 9 9 + 1x + 4x + -2x = 3(2 + 1x) * 3x + 2(4 + 1x) + -2 Combine like terms: 1x + 4x = 5x 9 + 5x + -2x = 3(2 + 1x) * 3x + 2(4 + 1x) + -2 Combine like terms: 5x + -2x = 3x 9 + 3x = 3(2 + 1x) * 3x + 2(4 + 1x) + -2 Reorder the terms for easier multiplication: 9 + 3x = 3 * 3x(2 + 1x) + 2(4 + 1x) + -2 Multiply 3 * 3 9 + 3x = 9x(2 + 1x) + 2(4 + 1x) + -2 9 + 3x = (2 * 9x + 1x * 9x) + 2(4 + 1x) + -2 9 + 3x = (18x + 9x2) + 2(4 + 1x) + -2 9 + 3x = 18x + 9x2 + (4 * 2 + 1x * 2) + -2 9 + 3x = 18x + 9x2 + (8 + 2x) + -2 Reorder the terms: 9 + 3x = 8 + -2 + 18x + 2x + 9x2 Combine like terms: 8 + -2 = 6 9 + 3x = 6 + 18x + 2x + 9x2 Combine like terms: 18x + 2x = 20x 9 + 3x = 6 + 20x + 9x2 Solving 9 + 3x = 6 + 20x + 9x2 Solving for variable 'x'. Reorder the terms: 9 + -6 + 3x + -20x + -9x2 = 6 + 20x + 9x2 + -6 + -20x + -9x2 Combine like terms: 9 + -6 = 3 3 + 3x + -20x + -9x2 = 6 + 20x + 9x2 + -6 + -20x + -9x2 Combine like terms: 3x + -20x = -17x 3 + -17x + -9x2 = 6 + 20x + 9x2 + -6 + -20x + -9x2 Reorder the terms: 3 + -17x + -9x2 = 6 + -6 + 20x + -20x + 9x2 + -9x2 Combine like terms: 6 + -6 = 0 3 + -17x + -9x2 = 0 + 20x + -20x + 9x2 + -9x2 3 + -17x + -9x2 = 20x + -20x + 9x2 + -9x2 Combine like terms: 20x + -20x = 0 3 + -17x + -9x2 = 0 + 9x2 + -9x2 3 + -17x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 3 + -17x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -0.3333333333 + 1.888888889x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 1.888888889x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 1.888888889x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 1.888888889x + x2 = 0 + 0.3333333333 1.888888889x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 1.888888889x + x2 = 0.3333333333 The x term is 1.888888889x. Take half its coefficient (0.9444444445). Square it (0.8919753087) and add it to both sides. Add '0.8919753087' to each side of the equation. 1.888888889x + 0.8919753087 + x2 = 0.3333333333 + 0.8919753087 Reorder the terms: 0.8919753087 + 1.888888889x + x2 = 0.3333333333 + 0.8919753087 Combine like terms: 0.3333333333 + 0.8919753087 = 1.225308642 0.8919753087 + 1.888888889x + x2 = 1.225308642 Factor a perfect square on the left side: (x + 0.9444444445)(x + 0.9444444445) = 1.225308642 Calculate the square root of the right side: 1.106936603 Break this problem into two subproblems by setting (x + 0.9444444445) equal to 1.106936603 and -1.106936603.Subproblem 1
x + 0.9444444445 = 1.106936603 Simplifying x + 0.9444444445 = 1.106936603 Reorder the terms: 0.9444444445 + x = 1.106936603 Solving 0.9444444445 + x = 1.106936603 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9444444445' to each side of the equation. 0.9444444445 + -0.9444444445 + x = 1.106936603 + -0.9444444445 Combine like terms: 0.9444444445 + -0.9444444445 = 0.0000000000 0.0000000000 + x = 1.106936603 + -0.9444444445 x = 1.106936603 + -0.9444444445 Combine like terms: 1.106936603 + -0.9444444445 = 0.1624921585 x = 0.1624921585 Simplifying x = 0.1624921585Subproblem 2
x + 0.9444444445 = -1.106936603 Simplifying x + 0.9444444445 = -1.106936603 Reorder the terms: 0.9444444445 + x = -1.106936603 Solving 0.9444444445 + x = -1.106936603 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9444444445' to each side of the equation. 0.9444444445 + -0.9444444445 + x = -1.106936603 + -0.9444444445 Combine like terms: 0.9444444445 + -0.9444444445 = 0.0000000000 0.0000000000 + x = -1.106936603 + -0.9444444445 x = -1.106936603 + -0.9444444445 Combine like terms: -1.106936603 + -0.9444444445 = -2.0513810475 x = -2.0513810475 Simplifying x = -2.0513810475Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1624921585, -2.0513810475}
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