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Simplifying 100x2 + -6x + -1.2 = 0 Reorder the terms: -1.2 + -6x + 100x2 = 0 Solving -1.2 + -6x + 100x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 100 the coefficient of the squared term: Divide each side by '100'. -0.012 + -0.06x + x2 = 0 Move the constant term to the right: Add '0.012' to each side of the equation. -0.012 + -0.06x + 0.012 + x2 = 0 + 0.012 Reorder the terms: -0.012 + 0.012 + -0.06x + x2 = 0 + 0.012 Combine like terms: -0.012 + 0.012 = 0.000 0.000 + -0.06x + x2 = 0 + 0.012 -0.06x + x2 = 0 + 0.012 Combine like terms: 0 + 0.012 = 0.012 -0.06x + x2 = 0.012 The x term is -0.06x. Take half its coefficient (-0.03). Square it (0.0009) and add it to both sides. Add '0.0009' to each side of the equation. -0.06x + 0.0009 + x2 = 0.012 + 0.0009 Reorder the terms: 0.0009 + -0.06x + x2 = 0.012 + 0.0009 Combine like terms: 0.012 + 0.0009 = 0.0129 0.0009 + -0.06x + x2 = 0.0129 Factor a perfect square on the left side: (x + -0.03)(x + -0.03) = 0.0129 Calculate the square root of the right side: 0.113578167 Break this problem into two subproblems by setting (x + -0.03) equal to 0.113578167 and -0.113578167.Subproblem 1
x + -0.03 = 0.113578167 Simplifying x + -0.03 = 0.113578167 Reorder the terms: -0.03 + x = 0.113578167 Solving -0.03 + x = 0.113578167 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03' to each side of the equation. -0.03 + 0.03 + x = 0.113578167 + 0.03 Combine like terms: -0.03 + 0.03 = 0.00 0.00 + x = 0.113578167 + 0.03 x = 0.113578167 + 0.03 Combine like terms: 0.113578167 + 0.03 = 0.143578167 x = 0.143578167 Simplifying x = 0.143578167Subproblem 2
x + -0.03 = -0.113578167 Simplifying x + -0.03 = -0.113578167 Reorder the terms: -0.03 + x = -0.113578167 Solving -0.03 + x = -0.113578167 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03' to each side of the equation. -0.03 + 0.03 + x = -0.113578167 + 0.03 Combine like terms: -0.03 + 0.03 = 0.00 0.00 + x = -0.113578167 + 0.03 x = -0.113578167 + 0.03 Combine like terms: -0.113578167 + 0.03 = -0.083578167 x = -0.083578167 Simplifying x = -0.083578167Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.143578167, -0.083578167}
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