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Simplifying 30x2 + -12x + 1 = 0 Reorder the terms: 1 + -12x + 30x2 = 0 Solving 1 + -12x + 30x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. 0.03333333333 + -0.4x + x2 = 0 Move the constant term to the right: Add '-0.03333333333' to each side of the equation. 0.03333333333 + -0.4x + -0.03333333333 + x2 = 0 + -0.03333333333 Reorder the terms: 0.03333333333 + -0.03333333333 + -0.4x + x2 = 0 + -0.03333333333 Combine like terms: 0.03333333333 + -0.03333333333 = 0.00000000000 0.00000000000 + -0.4x + x2 = 0 + -0.03333333333 -0.4x + x2 = 0 + -0.03333333333 Combine like terms: 0 + -0.03333333333 = -0.03333333333 -0.4x + x2 = -0.03333333333 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = -0.03333333333 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = -0.03333333333 + 0.04 Combine like terms: -0.03333333333 + 0.04 = 0.00666666667 0.04 + -0.4x + x2 = 0.00666666667 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 0.00666666667 Calculate the square root of the right side: 0.081649658 Break this problem into two subproblems by setting (x + -0.2) equal to 0.081649658 and -0.081649658.Subproblem 1
x + -0.2 = 0.081649658 Simplifying x + -0.2 = 0.081649658 Reorder the terms: -0.2 + x = 0.081649658 Solving -0.2 + x = 0.081649658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 0.081649658 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 0.081649658 + 0.2 x = 0.081649658 + 0.2 Combine like terms: 0.081649658 + 0.2 = 0.281649658 x = 0.281649658 Simplifying x = 0.281649658Subproblem 2
x + -0.2 = -0.081649658 Simplifying x + -0.2 = -0.081649658 Reorder the terms: -0.2 + x = -0.081649658 Solving -0.2 + x = -0.081649658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -0.081649658 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -0.081649658 + 0.2 x = -0.081649658 + 0.2 Combine like terms: -0.081649658 + 0.2 = 0.118350342 x = 0.118350342 Simplifying x = 0.118350342Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.281649658, 0.118350342}
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