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Simplifying (0.7 + -1x)(0.7 + -1x) = 0 Multiply (0.7 + -1x) * (0.7 + -1x) (0.7(0.7 + -1x) + -1x * (0.7 + -1x)) = 0 ((0.7 * 0.7 + -1x * 0.7) + -1x * (0.7 + -1x)) = 0 ((0.49 + -0.7x) + -1x * (0.7 + -1x)) = 0 (0.49 + -0.7x + (0.7 * -1x + -1x * -1x)) = 0 (0.49 + -0.7x + (-0.7x + 1x2)) = 0 Combine like terms: -0.7x + -0.7x = -1.4x (0.49 + -1.4x + 1x2) = 0 Solving 0.49 + -1.4x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.49' to each side of the equation. 0.49 + -1.4x + -0.49 + x2 = 0 + -0.49 Reorder the terms: 0.49 + -0.49 + -1.4x + x2 = 0 + -0.49 Combine like terms: 0.49 + -0.49 = 0.00 0.00 + -1.4x + x2 = 0 + -0.49 -1.4x + x2 = 0 + -0.49 Combine like terms: 0 + -0.49 = -0.49 -1.4x + x2 = -0.49 The x term is -1.4x. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4x + 0.49 + x2 = -0.49 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = -0.49 + 0.49 Combine like terms: -0.49 + 0.49 = 0.00 0.49 + -1.4x + x2 = 0.00 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (x + -0.7) equal to 0.00 and 0.00.Subproblem 1
x + -0.7 = 0.00 Simplifying x + -0.7 = 0.00 Reorder the terms: -0.7 + x = 0.00 Solving -0.7 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = 0.00 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 0.00 + 0.7 x = 0.00 + 0.7 Combine like terms: 0.00 + 0.7 = 0.7 x = 0.7 Simplifying x = 0.7Subproblem 2
x + -0.7 = 0.00 Simplifying x + -0.7 = 0.00 Reorder the terms: -0.7 + x = 0.00 Solving -0.7 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = 0.00 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 0.00 + 0.7 x = 0.00 + 0.7 Combine like terms: 0.00 + 0.7 = 0.7 x = 0.7 Simplifying x = 0.7Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7, 0.7}
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