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Simplifying 2.5x(x + -4) = 1.2(3x + -2) + 6 Reorder the terms: 2.5x(-4 + x) = 1.2(3x + -2) + 6 (-4 * 2.5x + x * 2.5x) = 1.2(3x + -2) + 6 (-10x + 2.5x2) = 1.2(3x + -2) + 6 Reorder the terms: -10x + 2.5x2 = 1.2(-2 + 3x) + 6 -10x + 2.5x2 = (-2 * 1.2 + 3x * 1.2) + 6 -10x + 2.5x2 = (-2.4 + 3.6x) + 6 Reorder the terms: -10x + 2.5x2 = -2.4 + 6 + 3.6x Combine like terms: -2.4 + 6 = 3.6 -10x + 2.5x2 = 3.6 + 3.6x Solving -10x + 2.5x2 = 3.6 + 3.6x Solving for variable 'x'. Reorder the terms: -3.6 + -10x + -3.6x + 2.5x2 = 3.6 + 3.6x + -3.6 + -3.6x Combine like terms: -10x + -3.6x = -13.6x -3.6 + -13.6x + 2.5x2 = 3.6 + 3.6x + -3.6 + -3.6x Reorder the terms: -3.6 + -13.6x + 2.5x2 = 3.6 + -3.6 + 3.6x + -3.6x Combine like terms: 3.6 + -3.6 = 0.0 -3.6 + -13.6x + 2.5x2 = 0.0 + 3.6x + -3.6x -3.6 + -13.6x + 2.5x2 = 3.6x + -3.6x Combine like terms: 3.6x + -3.6x = 0.0 -3.6 + -13.6x + 2.5x2 = 0.0 Begin completing the square. Divide all terms by 2.5 the coefficient of the squared term: Divide each side by '2.5'. -1.44 + -5.44x + x2 = 0 Move the constant term to the right: Add '1.44' to each side of the equation. -1.44 + -5.44x + 1.44 + x2 = 0 + 1.44 Reorder the terms: -1.44 + 1.44 + -5.44x + x2 = 0 + 1.44 Combine like terms: -1.44 + 1.44 = 0.00 0.00 + -5.44x + x2 = 0 + 1.44 -5.44x + x2 = 0 + 1.44 Combine like terms: 0 + 1.44 = 1.44 -5.44x + x2 = 1.44 The x term is -5.44x. Take half its coefficient (-2.72). Square it (7.3984) and add it to both sides. Add '7.3984' to each side of the equation. -5.44x + 7.3984 + x2 = 1.44 + 7.3984 Reorder the terms: 7.3984 + -5.44x + x2 = 1.44 + 7.3984 Combine like terms: 1.44 + 7.3984 = 8.8384 7.3984 + -5.44x + x2 = 8.8384 Factor a perfect square on the left side: (x + -2.72)(x + -2.72) = 8.8384 Calculate the square root of the right side: 2.972944668 Break this problem into two subproblems by setting (x + -2.72) equal to 2.972944668 and -2.972944668.Subproblem 1
x + -2.72 = 2.972944668 Simplifying x + -2.72 = 2.972944668 Reorder the terms: -2.72 + x = 2.972944668 Solving -2.72 + x = 2.972944668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.72' to each side of the equation. -2.72 + 2.72 + x = 2.972944668 + 2.72 Combine like terms: -2.72 + 2.72 = 0.00 0.00 + x = 2.972944668 + 2.72 x = 2.972944668 + 2.72 Combine like terms: 2.972944668 + 2.72 = 5.692944668 x = 5.692944668 Simplifying x = 5.692944668Subproblem 2
x + -2.72 = -2.972944668 Simplifying x + -2.72 = -2.972944668 Reorder the terms: -2.72 + x = -2.972944668 Solving -2.72 + x = -2.972944668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.72' to each side of the equation. -2.72 + 2.72 + x = -2.972944668 + 2.72 Combine like terms: -2.72 + 2.72 = 0.00 0.00 + x = -2.972944668 + 2.72 x = -2.972944668 + 2.72 Combine like terms: -2.972944668 + 2.72 = -0.252944668 x = -0.252944668 Simplifying x = -0.252944668Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.692944668, -0.252944668}
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