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Simplifying 0.36(0.36) + 1.2x + x(x) = 1 Multiply 0.36 * 0.36 0.1296 + 1.2x + x(x) = 1 Multiply x * x 0.1296 + 1.2x + x2 = 1 Solving 0.1296 + 1.2x + x2 = 1 Solving for variable 'x'. Reorder the terms: 0.1296 + -1 + 1.2x + x2 = 1 + -1 Combine like terms: 0.1296 + -1 = -0.8704 -0.8704 + 1.2x + x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -0.8704 + 1.2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '0.8704' to each side of the equation. -0.8704 + 1.2x + 0.8704 + x2 = 0 + 0.8704 Reorder the terms: -0.8704 + 0.8704 + 1.2x + x2 = 0 + 0.8704 Combine like terms: -0.8704 + 0.8704 = 0.0000 0.0000 + 1.2x + x2 = 0 + 0.8704 1.2x + x2 = 0 + 0.8704 Combine like terms: 0 + 0.8704 = 0.8704 1.2x + x2 = 0.8704 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 = 0.8704 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = 0.8704 + 0.36 Combine like terms: 0.8704 + 0.36 = 1.2304 0.36 + 1.2x + x2 = 1.2304 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 1.2304 Calculate the square root of the right side: 1.10923397 Break this problem into two subproblems by setting (x + 0.6) equal to 1.10923397 and -1.10923397.Subproblem 1
x + 0.6 = 1.10923397 Simplifying x + 0.6 = 1.10923397 Reorder the terms: 0.6 + x = 1.10923397 Solving 0.6 + x = 1.10923397 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 = 1.10923397 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 1.10923397 + -0.6 x = 1.10923397 + -0.6 Combine like terms: 1.10923397 + -0.6 = 0.50923397 x = 0.50923397 Simplifying x = 0.50923397Subproblem 2
x + 0.6 = -1.10923397 Simplifying x + 0.6 = -1.10923397 Reorder the terms: 0.6 + x = -1.10923397 Solving 0.6 + x = -1.10923397 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 = -1.10923397 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -1.10923397 + -0.6 x = -1.10923397 + -0.6 Combine like terms: -1.10923397 + -0.6 = -1.70923397 x = -1.70923397 Simplifying x = -1.70923397Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.50923397, -1.70923397}
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