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Simplifying x2 + 1.2x + 0.56 = 0.91 Reorder the terms: 0.56 + 1.2x + x2 = 0.91 Solving 0.56 + 1.2x + x2 = 0.91 Solving for variable 'x'. Reorder the terms: 0.56 + -0.91 + 1.2x + x2 = 0.91 + -0.91 Combine like terms: 0.56 + -0.91 = -0.35 -0.35 + 1.2x + x2 = 0.91 + -0.91 Combine like terms: 0.91 + -0.91 = 0.00 -0.35 + 1.2x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '0.35' to each side of the equation. -0.35 + 1.2x + 0.35 + x2 = 0.00 + 0.35 Reorder the terms: -0.35 + 0.35 + 1.2x + x2 = 0.00 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + 1.2x + x2 = 0.00 + 0.35 1.2x + x2 = 0.00 + 0.35 Combine like terms: 0.00 + 0.35 = 0.35 1.2x + x2 = 0.35 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 = 0.35 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = 0.35 + 0.36 Combine like terms: 0.35 + 0.36 = 0.71 0.36 + 1.2x + x2 = 0.71 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 0.71 Calculate the square root of the right side: 0.842614977 Break this problem into two subproblems by setting (x + 0.6) equal to 0.842614977 and -0.842614977.Subproblem 1
x + 0.6 = 0.842614977 Simplifying x + 0.6 = 0.842614977 Reorder the terms: 0.6 + x = 0.842614977 Solving 0.6 + x = 0.842614977 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 = 0.842614977 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 0.842614977 + -0.6 x = 0.842614977 + -0.6 Combine like terms: 0.842614977 + -0.6 = 0.242614977 x = 0.242614977 Simplifying x = 0.242614977Subproblem 2
x + 0.6 = -0.842614977 Simplifying x + 0.6 = -0.842614977 Reorder the terms: 0.6 + x = -0.842614977 Solving 0.6 + x = -0.842614977 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 = -0.842614977 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -0.842614977 + -0.6 x = -0.842614977 + -0.6 Combine like terms: -0.842614977 + -0.6 = -1.442614977 x = -1.442614977 Simplifying x = -1.442614977Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.242614977, -1.442614977}
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