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Simplifying 0.03x2 + 0.05x = 0.90 Reorder the terms: 0.05x + 0.03x2 = 0.90 Solving 0.05x + 0.03x2 = 0.90 Solving for variable 'x'. Reorder the terms: -0.90 + 0.05x + 0.03x2 = 0.90 + -0.90 Combine like terms: 0.90 + -0.90 = 0.00 -0.90 + 0.05x + 0.03x2 = 0.00 Begin completing the square. Divide all terms by 0.03 the coefficient of the squared term: Divide each side by '0.03'. -30 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + 1.666666667x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 1.666666667x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 1.666666667x + x2 = 0 + 30 1.666666667x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 1.666666667x + x2 = 30 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 30 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 30 + 0.6944444447 Combine like terms: 30 + 0.6944444447 = 30.6944444447 0.6944444447 + 1.666666667x + x2 = 30.6944444447 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 30.6944444447 Calculate the square root of the right side: 5.540256713 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 5.540256713 and -5.540256713.Subproblem 1
x + 0.8333333335 = 5.540256713 Simplifying x + 0.8333333335 = 5.540256713 Reorder the terms: 0.8333333335 + x = 5.540256713 Solving 0.8333333335 + x = 5.540256713 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 5.540256713 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 5.540256713 + -0.8333333335 x = 5.540256713 + -0.8333333335 Combine like terms: 5.540256713 + -0.8333333335 = 4.7069233795 x = 4.7069233795 Simplifying x = 4.7069233795Subproblem 2
x + 0.8333333335 = -5.540256713 Simplifying x + 0.8333333335 = -5.540256713 Reorder the terms: 0.8333333335 + x = -5.540256713 Solving 0.8333333335 + x = -5.540256713 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -5.540256713 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -5.540256713 + -0.8333333335 x = -5.540256713 + -0.8333333335 Combine like terms: -5.540256713 + -0.8333333335 = -6.3735900465 x = -6.3735900465 Simplifying x = -6.3735900465Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.7069233795, -6.3735900465}
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