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Simplifying (0.7 + -2x)(0.7 + -2x) = 0 Multiply (0.7 + -2x) * (0.7 + -2x) (0.7(0.7 + -2x) + -2x * (0.7 + -2x)) = 0 ((0.7 * 0.7 + -2x * 0.7) + -2x * (0.7 + -2x)) = 0 ((0.49 + -1.4x) + -2x * (0.7 + -2x)) = 0 (0.49 + -1.4x + (0.7 * -2x + -2x * -2x)) = 0 (0.49 + -1.4x + (-1.4x + 4x2)) = 0 Combine like terms: -1.4x + -1.4x = -2.8x (0.49 + -2.8x + 4x2) = 0 Solving 0.49 + -2.8x + 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'. 0.1225 + -0.7x + x2 = 0 Move the constant term to the right: Add '-0.1225' to each side of the equation. 0.1225 + -0.7x + -0.1225 + x2 = 0 + -0.1225 Reorder the terms: 0.1225 + -0.1225 + -0.7x + x2 = 0 + -0.1225 Combine like terms: 0.1225 + -0.1225 = 0.0000 0.0000 + -0.7x + x2 = 0 + -0.1225 -0.7x + x2 = 0 + -0.1225 Combine like terms: 0 + -0.1225 = -0.1225 -0.7x + x2 = -0.1225 The x term is -0.7x. Take half its coefficient (-0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. -0.7x + 0.1225 + x2 = -0.1225 + 0.1225 Reorder the terms: 0.1225 + -0.7x + x2 = -0.1225 + 0.1225 Combine like terms: -0.1225 + 0.1225 = 0.0000 0.1225 + -0.7x + x2 = 0.0000 Factor a perfect square on the left side: (x + -0.35)(x + -0.35) = 0.0000 Calculate the square root of the right side: 0.0000 Break this problem into two subproblems by setting (x + -0.35) equal to 0.0000 and 0.0000.Subproblem 1
x + -0.35 = 0.0000 Simplifying x + -0.35 = 0.0000 Reorder the terms: -0.35 + x = 0.0000 Solving -0.35 + x = 0.0000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + x = 0.0000 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + x = 0.0000 + 0.35 x = 0.0000 + 0.35 Combine like terms: 0.0000 + 0.35 = 0.35 x = 0.35 Simplifying x = 0.35Subproblem 2
x + -0.35 = 0.0000 Simplifying x + -0.35 = 0.0000 Reorder the terms: -0.35 + x = 0.0000 Solving -0.35 + x = 0.0000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + x = 0.0000 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + x = 0.0000 + 0.35 x = 0.0000 + 0.35 Combine like terms: 0.0000 + 0.35 = 0.35 x = 0.35 Simplifying x = 0.35Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.35, 0.35}
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