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Simplifying (2.6 + -2x)(2.6 + -2x) = 0 Multiply (2.6 + -2x) * (2.6 + -2x) (2.6(2.6 + -2x) + -2x * (2.6 + -2x)) = 0 ((2.6 * 2.6 + -2x * 2.6) + -2x * (2.6 + -2x)) = 0 ((6.76 + -5.2x) + -2x * (2.6 + -2x)) = 0 (6.76 + -5.2x + (2.6 * -2x + -2x * -2x)) = 0 (6.76 + -5.2x + (-5.2x + 4x2)) = 0 Combine like terms: -5.2x + -5.2x = -10.4x (6.76 + -10.4x + 4x2) = 0 Solving 6.76 + -10.4x + 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'. 1.69 + -2.6x + x2 = 0 Move the constant term to the right: Add '-1.69' to each side of the equation. 1.69 + -2.6x + -1.69 + x2 = 0 + -1.69 Reorder the terms: 1.69 + -1.69 + -2.6x + x2 = 0 + -1.69 Combine like terms: 1.69 + -1.69 = 0.00 0.00 + -2.6x + x2 = 0 + -1.69 -2.6x + x2 = 0 + -1.69 Combine like terms: 0 + -1.69 = -1.69 -2.6x + x2 = -1.69 The x term is -2.6x. Take half its coefficient (-1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. -2.6x + 1.69 + x2 = -1.69 + 1.69 Reorder the terms: 1.69 + -2.6x + x2 = -1.69 + 1.69 Combine like terms: -1.69 + 1.69 = 0.00 1.69 + -2.6x + x2 = 0.00 Factor a perfect square on the left side: (x + -1.3)(x + -1.3) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (x + -1.3) equal to 0.00 and 0.00.Subproblem 1
x + -1.3 = 0.00 Simplifying x + -1.3 = 0.00 Reorder the terms: -1.3 + x = 0.00 Solving -1.3 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + x = 0.00 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + x = 0.00 + 1.3 x = 0.00 + 1.3 Combine like terms: 0.00 + 1.3 = 1.3 x = 1.3 Simplifying x = 1.3Subproblem 2
x + -1.3 = 0.00 Simplifying x + -1.3 = 0.00 Reorder the terms: -1.3 + x = 0.00 Solving -1.3 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + x = 0.00 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + x = 0.00 + 1.3 x = 0.00 + 1.3 Combine like terms: 0.00 + 1.3 = 1.3 x = 1.3 Simplifying x = 1.3Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3, 1.3}
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