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Simplifying (3.4 + -2x)(3.4 + -2x) = 0 Multiply (3.4 + -2x) * (3.4 + -2x) (3.4(3.4 + -2x) + -2x * (3.4 + -2x)) = 0 ((3.4 * 3.4 + -2x * 3.4) + -2x * (3.4 + -2x)) = 0 ((11.56 + -6.8x) + -2x * (3.4 + -2x)) = 0 (11.56 + -6.8x + (3.4 * -2x + -2x * -2x)) = 0 (11.56 + -6.8x + (-6.8x + 4x2)) = 0 Combine like terms: -6.8x + -6.8x = -13.6x (11.56 + -13.6x + 4x2) = 0 Solving 11.56 + -13.6x + 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'. 2.89 + -3.4x + x2 = 0 Move the constant term to the right: Add '-2.89' to each side of the equation. 2.89 + -3.4x + -2.89 + x2 = 0 + -2.89 Reorder the terms: 2.89 + -2.89 + -3.4x + x2 = 0 + -2.89 Combine like terms: 2.89 + -2.89 = 0.00 0.00 + -3.4x + x2 = 0 + -2.89 -3.4x + x2 = 0 + -2.89 Combine like terms: 0 + -2.89 = -2.89 -3.4x + x2 = -2.89 The x term is -3.4x. Take half its coefficient (-1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. -3.4x + 2.89 + x2 = -2.89 + 2.89 Reorder the terms: 2.89 + -3.4x + x2 = -2.89 + 2.89 Combine like terms: -2.89 + 2.89 = 0.00 2.89 + -3.4x + x2 = 0.00 Factor a perfect square on the left side: (x + -1.7)(x + -1.7) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (x + -1.7) equal to 0.00 and 0.00.Subproblem 1
x + -1.7 = 0.00 Simplifying x + -1.7 = 0.00 Reorder the terms: -1.7 + x = 0.00 Solving -1.7 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + x = 0.00 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = 0.00 + 1.7 x = 0.00 + 1.7 Combine like terms: 0.00 + 1.7 = 1.7 x = 1.7 Simplifying x = 1.7Subproblem 2
x + -1.7 = 0.00 Simplifying x + -1.7 = 0.00 Reorder the terms: -1.7 + x = 0.00 Solving -1.7 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + x = 0.00 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = 0.00 + 1.7 x = 0.00 + 1.7 Combine like terms: 0.00 + 1.7 = 1.7 x = 1.7 Simplifying x = 1.7Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7, 1.7}
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