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Simplifying x2 + -1.2x + 0.36 = 0 Reorder the terms: 0.36 + -1.2x + x2 = 0 Solving 0.36 + -1.2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.36' to each side of the equation. 0.36 + -1.2x + -0.36 + x2 = 0 + -0.36 Reorder the terms: 0.36 + -0.36 + -1.2x + x2 = 0 + -0.36 Combine like terms: 0.36 + -0.36 = 0.00 0.00 + -1.2x + x2 = 0 + -0.36 -1.2x + x2 = 0 + -0.36 Combine like terms: 0 + -0.36 = -0.36 -1.2x + x2 = -0.36 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = -0.36 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = -0.36 + 0.36 Combine like terms: -0.36 + 0.36 = 0.00 0.36 + -1.2x + x2 = 0.00 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (x + -0.6) equal to 0.00 and 0.00.Subproblem 1
x + -0.6 = 0.00 Simplifying x + -0.6 = 0.00 Reorder the terms: -0.6 + x = 0.00 Solving -0.6 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 0.00 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 0.00 + 0.6 x = 0.00 + 0.6 Combine like terms: 0.00 + 0.6 = 0.6 x = 0.6 Simplifying x = 0.6Subproblem 2
x + -0.6 = 0.00 Simplifying x + -0.6 = 0.00 Reorder the terms: -0.6 + x = 0.00 Solving -0.6 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 0.00 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 0.00 + 0.6 x = 0.00 + 0.6 Combine like terms: 0.00 + 0.6 = 0.6 x = 0.6 Simplifying x = 0.6Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6, 0.6}
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