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Simplifying -0.05x2 + 0.6x + 2 = 0 Reorder the terms: 2 + 0.6x + -0.05x2 = 0 Solving 2 + 0.6x + -0.05x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.05 the coefficient of the squared term: Divide each side by '-0.05'. -40 + -12x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + -12x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + -12x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -12x + x2 = 0 + 40 -12x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 -12x + x2 = 40 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 40 + 36 Reorder the terms: 36 + -12x + x2 = 40 + 36 Combine like terms: 40 + 36 = 76 36 + -12x + x2 = 76 Factor a perfect square on the left side: (x + -6)(x + -6) = 76 Calculate the square root of the right side: 8.717797887 Break this problem into two subproblems by setting (x + -6) equal to 8.717797887 and -8.717797887.Subproblem 1
x + -6 = 8.717797887 Simplifying x + -6 = 8.717797887 Reorder the terms: -6 + x = 8.717797887 Solving -6 + x = 8.717797887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 8.717797887 + 6 Combine like terms: -6 + 6 = 0 0 + x = 8.717797887 + 6 x = 8.717797887 + 6 Combine like terms: 8.717797887 + 6 = 14.717797887 x = 14.717797887 Simplifying x = 14.717797887Subproblem 2
x + -6 = -8.717797887 Simplifying x + -6 = -8.717797887 Reorder the terms: -6 + x = -8.717797887 Solving -6 + x = -8.717797887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -8.717797887 + 6 Combine like terms: -6 + 6 = 0 0 + x = -8.717797887 + 6 x = -8.717797887 + 6 Combine like terms: -8.717797887 + 6 = -2.717797887 x = -2.717797887 Simplifying x = -2.717797887Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.717797887, -2.717797887}
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