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Simplifying -5x2 + 14.1x + -9.9 = 0 Reorder the terms: -9.9 + 14.1x + -5x2 = 0 Solving -9.9 + 14.1x + -5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 1.98 + -2.82x + x2 = 0 Move the constant term to the right: Add '-1.98' to each side of the equation. 1.98 + -2.82x + -1.98 + x2 = 0 + -1.98 Reorder the terms: 1.98 + -1.98 + -2.82x + x2 = 0 + -1.98 Combine like terms: 1.98 + -1.98 = 0.00 0.00 + -2.82x + x2 = 0 + -1.98 -2.82x + x2 = 0 + -1.98 Combine like terms: 0 + -1.98 = -1.98 -2.82x + x2 = -1.98 The x term is -2.82x. Take half its coefficient (-1.41). Square it (1.9881) and add it to both sides. Add '1.9881' to each side of the equation. -2.82x + 1.9881 + x2 = -1.98 + 1.9881 Reorder the terms: 1.9881 + -2.82x + x2 = -1.98 + 1.9881 Combine like terms: -1.98 + 1.9881 = 0.0081 1.9881 + -2.82x + x2 = 0.0081 Factor a perfect square on the left side: (x + -1.41)(x + -1.41) = 0.0081 Calculate the square root of the right side: 0.09 Break this problem into two subproblems by setting (x + -1.41) equal to 0.09 and -0.09.Subproblem 1
x + -1.41 = 0.09 Simplifying x + -1.41 = 0.09 Reorder the terms: -1.41 + x = 0.09 Solving -1.41 + x = 0.09 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.41' to each side of the equation. -1.41 + 1.41 + x = 0.09 + 1.41 Combine like terms: -1.41 + 1.41 = 0.00 0.00 + x = 0.09 + 1.41 x = 0.09 + 1.41 Combine like terms: 0.09 + 1.41 = 1.5 x = 1.5 Simplifying x = 1.5Subproblem 2
x + -1.41 = -0.09 Simplifying x + -1.41 = -0.09 Reorder the terms: -1.41 + x = -0.09 Solving -1.41 + x = -0.09 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.41' to each side of the equation. -1.41 + 1.41 + x = -0.09 + 1.41 Combine like terms: -1.41 + 1.41 = 0.00 0.00 + x = -0.09 + 1.41 x = -0.09 + 1.41 Combine like terms: -0.09 + 1.41 = 1.32 x = 1.32 Simplifying x = 1.32Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5, 1.32}
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