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Simplifying (7.6 + -2x)(7.6 + -2x) = 0 Multiply (7.6 + -2x) * (7.6 + -2x) (7.6(7.6 + -2x) + -2x * (7.6 + -2x)) = 0 ((7.6 * 7.6 + -2x * 7.6) + -2x * (7.6 + -2x)) = 0 ((57.76 + -15.2x) + -2x * (7.6 + -2x)) = 0 (57.76 + -15.2x + (7.6 * -2x + -2x * -2x)) = 0 (57.76 + -15.2x + (-15.2x + 4x2)) = 0 Combine like terms: -15.2x + -15.2x = -30.4x (57.76 + -30.4x + 4x2) = 0 Solving 57.76 + -30.4x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 14.44 + -7.6x + x2 = 0 Move the constant term to the right: Add '-14.44' to each side of the equation. 14.44 + -7.6x + -14.44 + x2 = 0 + -14.44 Reorder the terms: 14.44 + -14.44 + -7.6x + x2 = 0 + -14.44 Combine like terms: 14.44 + -14.44 = 0.00 0.00 + -7.6x + x2 = 0 + -14.44 -7.6x + x2 = 0 + -14.44 Combine like terms: 0 + -14.44 = -14.44 -7.6x + x2 = -14.44 The x term is -7.6x. Take half its coefficient (-3.8). Square it (14.44) and add it to both sides. Add '14.44' to each side of the equation. -7.6x + 14.44 + x2 = -14.44 + 14.44 Reorder the terms: 14.44 + -7.6x + x2 = -14.44 + 14.44 Combine like terms: -14.44 + 14.44 = 0.00 14.44 + -7.6x + x2 = 0.00 Factor a perfect square on the left side: (x + -3.8)(x + -3.8) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (x + -3.8) equal to 0.00 and 0.00.Subproblem 1
x + -3.8 = 0.00 Simplifying x + -3.8 = 0.00 Reorder the terms: -3.8 + x = 0.00 Solving -3.8 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.8' to each side of the equation. -3.8 + 3.8 + x = 0.00 + 3.8 Combine like terms: -3.8 + 3.8 = 0.0 0.0 + x = 0.00 + 3.8 x = 0.00 + 3.8 Combine like terms: 0.00 + 3.8 = 3.8 x = 3.8 Simplifying x = 3.8Subproblem 2
x + -3.8 = 0.00 Simplifying x + -3.8 = 0.00 Reorder the terms: -3.8 + x = 0.00 Solving -3.8 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.8' to each side of the equation. -3.8 + 3.8 + x = 0.00 + 3.8 Combine like terms: -3.8 + 3.8 = 0.0 0.0 + x = 0.00 + 3.8 x = 0.00 + 3.8 Combine like terms: 0.00 + 3.8 = 3.8 x = 3.8 Simplifying x = 3.8Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.8, 3.8}
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