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Simplifying x2 + 0.016x + -0.016 = 0 Reorder the terms: -0.016 + 0.016x + x2 = 0 Solving -0.016 + 0.016x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.016' to each side of the equation. -0.016 + 0.016x + 0.016 + x2 = 0 + 0.016 Reorder the terms: -0.016 + 0.016 + 0.016x + x2 = 0 + 0.016 Combine like terms: -0.016 + 0.016 = 0.000 0.000 + 0.016x + x2 = 0 + 0.016 0.016x + x2 = 0 + 0.016 Combine like terms: 0 + 0.016 = 0.016 0.016x + x2 = 0.016 The x term is 0.016x. Take half its coefficient (0.008). Square it (0.000064) and add it to both sides. Add '0.000064' to each side of the equation. 0.016x + 0.000064 + x2 = 0.016 + 0.000064 Reorder the terms: 0.000064 + 0.016x + x2 = 0.016 + 0.000064 Combine like terms: 0.016 + 0.000064 = 0.016064 0.000064 + 0.016x + x2 = 0.016064 Factor a perfect square on the left side: (x + 0.008)(x + 0.008) = 0.016064 Calculate the square root of the right side: 0.126743836 Break this problem into two subproblems by setting (x + 0.008) equal to 0.126743836 and -0.126743836.Subproblem 1
x + 0.008 = 0.126743836 Simplifying x + 0.008 = 0.126743836 Reorder the terms: 0.008 + x = 0.126743836 Solving 0.008 + x = 0.126743836 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.008' to each side of the equation. 0.008 + -0.008 + x = 0.126743836 + -0.008 Combine like terms: 0.008 + -0.008 = 0.000 0.000 + x = 0.126743836 + -0.008 x = 0.126743836 + -0.008 Combine like terms: 0.126743836 + -0.008 = 0.118743836 x = 0.118743836 Simplifying x = 0.118743836Subproblem 2
x + 0.008 = -0.126743836 Simplifying x + 0.008 = -0.126743836 Reorder the terms: 0.008 + x = -0.126743836 Solving 0.008 + x = -0.126743836 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.008' to each side of the equation. 0.008 + -0.008 + x = -0.126743836 + -0.008 Combine like terms: 0.008 + -0.008 = 0.000 0.000 + x = -0.126743836 + -0.008 x = -0.126743836 + -0.008 Combine like terms: -0.126743836 + -0.008 = -0.134743836 x = -0.134743836 Simplifying x = -0.134743836Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.118743836, -0.134743836}
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