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Simplifying x2 = 0.1537 + -0.849x Solving x2 = 0.1537 + -0.849x Solving for variable 'x'. Reorder the terms: -0.1537 + 0.849x + x2 = 0.1537 + -0.849x + -0.1537 + 0.849x Reorder the terms: -0.1537 + 0.849x + x2 = 0.1537 + -0.1537 + -0.849x + 0.849x Combine like terms: 0.1537 + -0.1537 = 0.0000 -0.1537 + 0.849x + x2 = 0.0000 + -0.849x + 0.849x -0.1537 + 0.849x + x2 = -0.849x + 0.849x Combine like terms: -0.849x + 0.849x = 0.000 -0.1537 + 0.849x + x2 = 0.000 Begin completing the square. Move the constant term to the right: Add '0.1537' to each side of the equation. -0.1537 + 0.849x + 0.1537 + x2 = 0.000 + 0.1537 Reorder the terms: -0.1537 + 0.1537 + 0.849x + x2 = 0.000 + 0.1537 Combine like terms: -0.1537 + 0.1537 = 0.0000 0.0000 + 0.849x + x2 = 0.000 + 0.1537 0.849x + x2 = 0.000 + 0.1537 Combine like terms: 0.000 + 0.1537 = 0.1537 0.849x + x2 = 0.1537 The x term is 0.849x. Take half its coefficient (0.4245). Square it (0.18020025) and add it to both sides. Add '0.18020025' to each side of the equation. 0.849x + 0.18020025 + x2 = 0.1537 + 0.18020025 Reorder the terms: 0.18020025 + 0.849x + x2 = 0.1537 + 0.18020025 Combine like terms: 0.1537 + 0.18020025 = 0.33390025 0.18020025 + 0.849x + x2 = 0.33390025 Factor a perfect square on the left side: (x + 0.4245)(x + 0.4245) = 0.33390025 Calculate the square root of the right side: 0.577841025 Break this problem into two subproblems by setting (x + 0.4245) equal to 0.577841025 and -0.577841025.Subproblem 1
x + 0.4245 = 0.577841025 Simplifying x + 0.4245 = 0.577841025 Reorder the terms: 0.4245 + x = 0.577841025 Solving 0.4245 + x = 0.577841025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4245' to each side of the equation. 0.4245 + -0.4245 + x = 0.577841025 + -0.4245 Combine like terms: 0.4245 + -0.4245 = 0.0000 0.0000 + x = 0.577841025 + -0.4245 x = 0.577841025 + -0.4245 Combine like terms: 0.577841025 + -0.4245 = 0.153341025 x = 0.153341025 Simplifying x = 0.153341025Subproblem 2
x + 0.4245 = -0.577841025 Simplifying x + 0.4245 = -0.577841025 Reorder the terms: 0.4245 + x = -0.577841025 Solving 0.4245 + x = -0.577841025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4245' to each side of the equation. 0.4245 + -0.4245 + x = -0.577841025 + -0.4245 Combine like terms: 0.4245 + -0.4245 = 0.0000 0.0000 + x = -0.577841025 + -0.4245 x = -0.577841025 + -0.4245 Combine like terms: -0.577841025 + -0.4245 = -1.002341025 x = -1.002341025 Simplifying x = -1.002341025Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.153341025, -1.002341025}
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