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Simplifying x2 = 0.00667 + -1x Solving x2 = 0.00667 + -1x Solving for variable 'x'. Reorder the terms: -0.00667 + x + x2 = 0.00667 + -1x + -0.00667 + x Reorder the terms: -0.00667 + x + x2 = 0.00667 + -0.00667 + -1x + x Combine like terms: 0.00667 + -0.00667 = 0.00000 -0.00667 + x + x2 = 0.00000 + -1x + x -0.00667 + x + x2 = -1x + x Combine like terms: -1x + x = 0 -0.00667 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '0.00667' to each side of the equation. -0.00667 + x + 0.00667 + x2 = 0 + 0.00667 Reorder the terms: -0.00667 + 0.00667 + x + x2 = 0 + 0.00667 Combine like terms: -0.00667 + 0.00667 = 0.00000 0.00000 + x + x2 = 0 + 0.00667 x + x2 = 0 + 0.00667 Combine like terms: 0 + 0.00667 = 0.00667 x + x2 = 0.00667 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 0.00667 + 0.25 Reorder the terms: 0.25 + x + x2 = 0.00667 + 0.25 Combine like terms: 0.00667 + 0.25 = 0.25667 0.25 + x + x2 = 0.25667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.25667 Calculate the square root of the right side: 0.506626095 Break this problem into two subproblems by setting (x + 0.5) equal to 0.506626095 and -0.506626095.Subproblem 1
x + 0.5 = 0.506626095 Simplifying x + 0.5 = 0.506626095 Reorder the terms: 0.5 + x = 0.506626095 Solving 0.5 + x = 0.506626095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.506626095 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.506626095 + -0.5 x = 0.506626095 + -0.5 Combine like terms: 0.506626095 + -0.5 = 0.006626095 x = 0.006626095 Simplifying x = 0.006626095Subproblem 2
x + 0.5 = -0.506626095 Simplifying x + 0.5 = -0.506626095 Reorder the terms: 0.5 + x = -0.506626095 Solving 0.5 + x = -0.506626095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.506626095 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.506626095 + -0.5 x = -0.506626095 + -0.5 Combine like terms: -0.506626095 + -0.5 = -1.006626095 x = -1.006626095 Simplifying x = -1.006626095Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.006626095, -1.006626095}
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