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Simplifying (2.5x + -5)(6x + 1.8) = 0 Reorder the terms: (-5 + 2.5x)(6x + 1.8) = 0 Reorder the terms: (-5 + 2.5x)(1.8 + 6x) = 0 Multiply (-5 + 2.5x) * (1.8 + 6x) (-5(1.8 + 6x) + 2.5x * (1.8 + 6x)) = 0 ((1.8 * -5 + 6x * -5) + 2.5x * (1.8 + 6x)) = 0 ((-9 + -30x) + 2.5x * (1.8 + 6x)) = 0 (-9 + -30x + (1.8 * 2.5x + 6x * 2.5x)) = 0 (-9 + -30x + (4.5x + 15x2)) = 0 Combine like terms: -30x + 4.5x = -25.5x (-9 + -25.5x + 15x2) = 0 Solving -9 + -25.5x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.6 + -1.7x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -1.7x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -1.7x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -1.7x + x2 = 0 + 0.6 -1.7x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -1.7x + x2 = 0.6 The x term is -1.7x. Take half its coefficient (-0.85). Square it (0.7225) and add it to both sides. Add '0.7225' to each side of the equation. -1.7x + 0.7225 + x2 = 0.6 + 0.7225 Reorder the terms: 0.7225 + -1.7x + x2 = 0.6 + 0.7225 Combine like terms: 0.6 + 0.7225 = 1.3225 0.7225 + -1.7x + x2 = 1.3225 Factor a perfect square on the left side: (x + -0.85)(x + -0.85) = 1.3225 Calculate the square root of the right side: 1.15 Break this problem into two subproblems by setting (x + -0.85) equal to 1.15 and -1.15.Subproblem 1
x + -0.85 = 1.15 Simplifying x + -0.85 = 1.15 Reorder the terms: -0.85 + x = 1.15 Solving -0.85 + x = 1.15 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.85' to each side of the equation. -0.85 + 0.85 + x = 1.15 + 0.85 Combine like terms: -0.85 + 0.85 = 0.00 0.00 + x = 1.15 + 0.85 x = 1.15 + 0.85 Combine like terms: 1.15 + 0.85 = 2 x = 2 Simplifying x = 2Subproblem 2
x + -0.85 = -1.15 Simplifying x + -0.85 = -1.15 Reorder the terms: -0.85 + x = -1.15 Solving -0.85 + x = -1.15 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.85' to each side of the equation. -0.85 + 0.85 + x = -1.15 + 0.85 Combine like terms: -0.85 + 0.85 = 0.00 0.00 + x = -1.15 + 0.85 x = -1.15 + 0.85 Combine like terms: -1.15 + 0.85 = -0.3 x = -0.3 Simplifying x = -0.3Solution
The solution to the problem is based on the solutions from the subproblems. x = {2, -0.3}
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