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Simplifying 20x2 + 12x + 0.9 = 37 Reorder the terms: 0.9 + 12x + 20x2 = 37 Solving 0.9 + 12x + 20x2 = 37 Solving for variable 'x'. Reorder the terms: 0.9 + -37 + 12x + 20x2 = 37 + -37 Combine like terms: 0.9 + -37 = -36.1 -36.1 + 12x + 20x2 = 37 + -37 Combine like terms: 37 + -37 = 0 -36.1 + 12x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -1.805 + 0.6x + x2 = 0 Move the constant term to the right: Add '1.805' to each side of the equation. -1.805 + 0.6x + 1.805 + x2 = 0 + 1.805 Reorder the terms: -1.805 + 1.805 + 0.6x + x2 = 0 + 1.805 Combine like terms: -1.805 + 1.805 = 0.000 0.000 + 0.6x + x2 = 0 + 1.805 0.6x + x2 = 0 + 1.805 Combine like terms: 0 + 1.805 = 1.805 0.6x + x2 = 1.805 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 = 1.805 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 1.805 + 0.09 Combine like terms: 1.805 + 0.09 = 1.895 0.09 + 0.6x + x2 = 1.895 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 1.895 Calculate the square root of the right side: 1.37658999 Break this problem into two subproblems by setting (x + 0.3) equal to 1.37658999 and -1.37658999.Subproblem 1
x + 0.3 = 1.37658999 Simplifying x + 0.3 = 1.37658999 Reorder the terms: 0.3 + x = 1.37658999 Solving 0.3 + x = 1.37658999 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 = 1.37658999 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 1.37658999 + -0.3 x = 1.37658999 + -0.3 Combine like terms: 1.37658999 + -0.3 = 1.07658999 x = 1.07658999 Simplifying x = 1.07658999Subproblem 2
x + 0.3 = -1.37658999 Simplifying x + 0.3 = -1.37658999 Reorder the terms: 0.3 + x = -1.37658999 Solving 0.3 + x = -1.37658999 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 = -1.37658999 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -1.37658999 + -0.3 x = -1.37658999 + -0.3 Combine like terms: -1.37658999 + -0.3 = -1.67658999 x = -1.67658999 Simplifying x = -1.67658999Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.07658999, -1.67658999}
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