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Simplifying 3x2 + 0.06x + -0.2519 = 0 Reorder the terms: -0.2519 + 0.06x + 3x2 = 0 Solving -0.2519 + 0.06x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.08396666667 + 0.02x + x2 = 0 Move the constant term to the right: Add '0.08396666667' to each side of the equation. -0.08396666667 + 0.02x + 0.08396666667 + x2 = 0 + 0.08396666667 Reorder the terms: -0.08396666667 + 0.08396666667 + 0.02x + x2 = 0 + 0.08396666667 Combine like terms: -0.08396666667 + 0.08396666667 = 0.00000000000 0.00000000000 + 0.02x + x2 = 0 + 0.08396666667 0.02x + x2 = 0 + 0.08396666667 Combine like terms: 0 + 0.08396666667 = 0.08396666667 0.02x + x2 = 0.08396666667 The x term is 0.02x. Take half its coefficient (0.01). Square it (0.0001) and add it to both sides. Add '0.0001' to each side of the equation. 0.02x + 0.0001 + x2 = 0.08396666667 + 0.0001 Reorder the terms: 0.0001 + 0.02x + x2 = 0.08396666667 + 0.0001 Combine like terms: 0.08396666667 + 0.0001 = 0.08406666667 0.0001 + 0.02x + x2 = 0.08406666667 Factor a perfect square on the left side: (x + 0.01)(x + 0.01) = 0.08406666667 Calculate the square root of the right side: 0.289942523 Break this problem into two subproblems by setting (x + 0.01) equal to 0.289942523 and -0.289942523.Subproblem 1
x + 0.01 = 0.289942523 Simplifying x + 0.01 = 0.289942523 Reorder the terms: 0.01 + x = 0.289942523 Solving 0.01 + x = 0.289942523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01' to each side of the equation. 0.01 + -0.01 + x = 0.289942523 + -0.01 Combine like terms: 0.01 + -0.01 = 0.00 0.00 + x = 0.289942523 + -0.01 x = 0.289942523 + -0.01 Combine like terms: 0.289942523 + -0.01 = 0.279942523 x = 0.279942523 Simplifying x = 0.279942523Subproblem 2
x + 0.01 = -0.289942523 Simplifying x + 0.01 = -0.289942523 Reorder the terms: 0.01 + x = -0.289942523 Solving 0.01 + x = -0.289942523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01' to each side of the equation. 0.01 + -0.01 + x = -0.289942523 + -0.01 Combine like terms: 0.01 + -0.01 = 0.00 0.00 + x = -0.289942523 + -0.01 x = -0.289942523 + -0.01 Combine like terms: -0.289942523 + -0.01 = -0.299942523 x = -0.299942523 Simplifying x = -0.299942523Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.279942523, -0.299942523}
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