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Simplifying 100x2 + -60x + -39 = 0 Reorder the terms: -39 + -60x + 100x2 = 0 Solving -39 + -60x + 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'. -0.39 + -0.6x + x2 = 0 Move the constant term to the right: Add '0.39' to each side of the equation. -0.39 + -0.6x + 0.39 + x2 = 0 + 0.39 Reorder the terms: -0.39 + 0.39 + -0.6x + x2 = 0 + 0.39 Combine like terms: -0.39 + 0.39 = 0.00 0.00 + -0.6x + x2 = 0 + 0.39 -0.6x + x2 = 0 + 0.39 Combine like terms: 0 + 0.39 = 0.39 -0.6x + x2 = 0.39 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 0.39 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 0.39 + 0.09 Combine like terms: 0.39 + 0.09 = 0.48 0.09 + -0.6x + x2 = 0.48 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 0.48 Calculate the square root of the right side: 0.692820323 Break this problem into two subproblems by setting (x + -0.3) equal to 0.692820323 and -0.692820323.Subproblem 1
x + -0.3 = 0.692820323 Simplifying x + -0.3 = 0.692820323 Reorder the terms: -0.3 + x = 0.692820323 Solving -0.3 + x = 0.692820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 0.692820323 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 0.692820323 + 0.3 x = 0.692820323 + 0.3 Combine like terms: 0.692820323 + 0.3 = 0.992820323 x = 0.992820323 Simplifying x = 0.992820323Subproblem 2
x + -0.3 = -0.692820323 Simplifying x + -0.3 = -0.692820323 Reorder the terms: -0.3 + x = -0.692820323 Solving -0.3 + x = -0.692820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -0.692820323 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -0.692820323 + 0.3 x = -0.692820323 + 0.3 Combine like terms: -0.692820323 + 0.3 = -0.392820323 x = -0.392820323 Simplifying x = -0.392820323Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.992820323, -0.392820323}
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