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Simplifying 150x2 = 0.3 + -1x Solving 150x2 = 0.3 + -1x Solving for variable 'x'. Reorder the terms: -0.3 + x + 150x2 = 0.3 + -1x + -0.3 + x Reorder the terms: -0.3 + x + 150x2 = 0.3 + -0.3 + -1x + x Combine like terms: 0.3 + -0.3 = 0.0 -0.3 + x + 150x2 = 0.0 + -1x + x -0.3 + x + 150x2 = -1x + x Combine like terms: -1x + x = 0 -0.3 + x + 150x2 = 0 Begin completing the square. Divide all terms by 150 the coefficient of the squared term: Divide each side by '150'. -0.002 + 0.006666666667x + x2 = 0 Move the constant term to the right: Add '0.002' to each side of the equation. -0.002 + 0.006666666667x + 0.002 + x2 = 0 + 0.002 Reorder the terms: -0.002 + 0.002 + 0.006666666667x + x2 = 0 + 0.002 Combine like terms: -0.002 + 0.002 = 0.000 0.000 + 0.006666666667x + x2 = 0 + 0.002 0.006666666667x + x2 = 0 + 0.002 Combine like terms: 0 + 0.002 = 0.002 0.006666666667x + x2 = 0.002 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. 0.006666666667x + 0.25 + x2 = 0.002 + 0.25 Reorder the terms: 0.25 + 0.006666666667x + x2 = 0.002 + 0.25 Combine like terms: 0.002 + 0.25 = 0.252 0.25 + 0.006666666667x + x2 = 0.252 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.252 Calculate the square root of the right side: 0.501996016 Break this problem into two subproblems by setting (x + 0.5) equal to 0.501996016 and -0.501996016.Subproblem 1
x + 0.5 = 0.501996016 Simplifying x + 0.5 = 0.501996016 Reorder the terms: 0.5 + x = 0.501996016 Solving 0.5 + x = 0.501996016 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 = 0.501996016 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.501996016 + -0.5 x = 0.501996016 + -0.5 Combine like terms: 0.501996016 + -0.5 = 0.001996016 x = 0.001996016 Simplifying x = 0.001996016Subproblem 2
x + 0.5 = -0.501996016 Simplifying x + 0.5 = -0.501996016 Reorder the terms: 0.5 + x = -0.501996016 Solving 0.5 + x = -0.501996016 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 = -0.501996016 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.501996016 + -0.5 x = -0.501996016 + -0.5 Combine like terms: -0.501996016 + -0.5 = -1.001996016 x = -1.001996016 Simplifying x = -1.001996016Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.001996016, -1.001996016}
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