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Simplifying (3x + -2x + 2)(5x + -4) = 6 Reorder the terms: (2 + 3x + -2x)(5x + -4) = 6 Combine like terms: 3x + -2x = 1x (2 + 1x)(5x + -4) = 6 Reorder the terms: (2 + 1x)(-4 + 5x) = 6 Multiply (2 + 1x) * (-4 + 5x) (2(-4 + 5x) + 1x * (-4 + 5x)) = 6 ((-4 * 2 + 5x * 2) + 1x * (-4 + 5x)) = 6 ((-8 + 10x) + 1x * (-4 + 5x)) = 6 (-8 + 10x + (-4 * 1x + 5x * 1x)) = 6 (-8 + 10x + (-4x + 5x2)) = 6 Combine like terms: 10x + -4x = 6x (-8 + 6x + 5x2) = 6 Solving -8 + 6x + 5x2 = 6 Solving for variable 'x'. Reorder the terms: -8 + -6 + 6x + 5x2 = 6 + -6 Combine like terms: -8 + -6 = -14 -14 + 6x + 5x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -14 + 6x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.8 + 1.2x + x2 = 0 Move the constant term to the right: Add '2.8' to each side of the equation. -2.8 + 1.2x + 2.8 + x2 = 0 + 2.8 Reorder the terms: -2.8 + 2.8 + 1.2x + x2 = 0 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + 1.2x + x2 = 0 + 2.8 1.2x + x2 = 0 + 2.8 Combine like terms: 0 + 2.8 = 2.8 1.2x + x2 = 2.8 The x term is 1.2x. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2x + 0.36 + x2 = 2.8 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = 2.8 + 0.36 Combine like terms: 2.8 + 0.36 = 3.16 0.36 + 1.2x + x2 = 3.16 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 3.16 Calculate the square root of the right side: 1.777638883 Break this problem into two subproblems by setting (x + 0.6) equal to 1.777638883 and -1.777638883.Subproblem 1
x + 0.6 = 1.777638883 Simplifying x + 0.6 = 1.777638883 Reorder the terms: 0.6 + x = 1.777638883 Solving 0.6 + x = 1.777638883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = 1.777638883 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 1.777638883 + -0.6 x = 1.777638883 + -0.6 Combine like terms: 1.777638883 + -0.6 = 1.177638883 x = 1.177638883 Simplifying x = 1.177638883Subproblem 2
x + 0.6 = -1.777638883 Simplifying x + 0.6 = -1.777638883 Reorder the terms: 0.6 + x = -1.777638883 Solving 0.6 + x = -1.777638883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = -1.777638883 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -1.777638883 + -0.6 x = -1.777638883 + -0.6 Combine like terms: -1.777638883 + -0.6 = -2.377638883 x = -2.377638883 Simplifying x = -2.377638883Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.177638883, -2.377638883}
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