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Simplifying 2x(x + -3) = 1.2 + x Reorder the terms: 2x(-3 + x) = 1.2 + x (-3 * 2x + x * 2x) = 1.2 + x (-6x + 2x2) = 1.2 + x Solving -6x + 2x2 = 1.2 + x Solving for variable 'x'. Reorder the terms: -1.2 + -6x + -1x + 2x2 = 1.2 + x + -1.2 + -1x Combine like terms: -6x + -1x = -7x -1.2 + -7x + 2x2 = 1.2 + x + -1.2 + -1x Reorder the terms: -1.2 + -7x + 2x2 = 1.2 + -1.2 + x + -1x Combine like terms: 1.2 + -1.2 = 0.0 -1.2 + -7x + 2x2 = 0.0 + x + -1x -1.2 + -7x + 2x2 = x + -1x Combine like terms: x + -1x = 0 -1.2 + -7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.6 + -3.5x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -3.5x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -3.5x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -3.5x + x2 = 0 + 0.6 -3.5x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -3.5x + x2 = 0.6 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 0.6 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 0.6 + 3.0625 Combine like terms: 0.6 + 3.0625 = 3.6625 3.0625 + -3.5x + x2 = 3.6625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 3.6625 Calculate the square root of the right side: 1.913765921 Break this problem into two subproblems by setting (x + -1.75) equal to 1.913765921 and -1.913765921.Subproblem 1
x + -1.75 = 1.913765921 Simplifying x + -1.75 = 1.913765921 Reorder the terms: -1.75 + x = 1.913765921 Solving -1.75 + x = 1.913765921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 1.913765921 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 1.913765921 + 1.75 x = 1.913765921 + 1.75 Combine like terms: 1.913765921 + 1.75 = 3.663765921 x = 3.663765921 Simplifying x = 3.663765921Subproblem 2
x + -1.75 = -1.913765921 Simplifying x + -1.75 = -1.913765921 Reorder the terms: -1.75 + x = -1.913765921 Solving -1.75 + x = -1.913765921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -1.913765921 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -1.913765921 + 1.75 x = -1.913765921 + 1.75 Combine like terms: -1.913765921 + 1.75 = -0.163765921 x = -0.163765921 Simplifying x = -0.163765921Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.663765921, -0.163765921}
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