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Simplifying (x2) = 1.8(0.3 + -1x) x2 = 1.8(0.3 + -1x) x2 = (0.3 * 1.8 + -1x * 1.8) x2 = (0.54 + -1.8x) Solving x2 = 0.54 + -1.8x Solving for variable 'x'. Reorder the terms: -0.54 + 1.8x + x2 = 0.54 + -1.8x + -0.54 + 1.8x Reorder the terms: -0.54 + 1.8x + x2 = 0.54 + -0.54 + -1.8x + 1.8x Combine like terms: 0.54 + -0.54 = 0.00 -0.54 + 1.8x + x2 = 0.00 + -1.8x + 1.8x -0.54 + 1.8x + x2 = -1.8x + 1.8x Combine like terms: -1.8x + 1.8x = 0.0 -0.54 + 1.8x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '0.54' to each side of the equation. -0.54 + 1.8x + 0.54 + x2 = 0.0 + 0.54 Reorder the terms: -0.54 + 0.54 + 1.8x + x2 = 0.0 + 0.54 Combine like terms: -0.54 + 0.54 = 0.00 0.00 + 1.8x + x2 = 0.0 + 0.54 1.8x + x2 = 0.0 + 0.54 Combine like terms: 0.0 + 0.54 = 0.54 1.8x + x2 = 0.54 The x term is 1.8x. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8x + 0.81 + x2 = 0.54 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = 0.54 + 0.81 Combine like terms: 0.54 + 0.81 = 1.35 0.81 + 1.8x + x2 = 1.35 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = 1.35 Calculate the square root of the right side: 1.161895004 Break this problem into two subproblems by setting (x + 0.9) equal to 1.161895004 and -1.161895004.Subproblem 1
x + 0.9 = 1.161895004 Simplifying x + 0.9 = 1.161895004 Reorder the terms: 0.9 + x = 1.161895004 Solving 0.9 + x = 1.161895004 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = 1.161895004 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 1.161895004 + -0.9 x = 1.161895004 + -0.9 Combine like terms: 1.161895004 + -0.9 = 0.261895004 x = 0.261895004 Simplifying x = 0.261895004Subproblem 2
x + 0.9 = -1.161895004 Simplifying x + 0.9 = -1.161895004 Reorder the terms: 0.9 + x = -1.161895004 Solving 0.9 + x = -1.161895004 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = -1.161895004 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -1.161895004 + -0.9 x = -1.161895004 + -0.9 Combine like terms: -1.161895004 + -0.9 = -2.061895004 x = -2.061895004 Simplifying x = -2.061895004Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.261895004, -2.061895004}
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