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Simplifying 3x2 + 0.25 + -3x = 0 Reorder the terms: 0.25 + -3x + 3x2 = 0 Solving 0.25 + -3x + 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'. 0.08333333333 + -1x + x2 = 0 Move the constant term to the right: Add '-0.08333333333' to each side of the equation. 0.08333333333 + -1x + -0.08333333333 + x2 = 0 + -0.08333333333 Reorder the terms: 0.08333333333 + -0.08333333333 + -1x + x2 = 0 + -0.08333333333 Combine like terms: 0.08333333333 + -0.08333333333 = 0.00000000000 0.00000000000 + -1x + x2 = 0 + -0.08333333333 -1x + x2 = 0 + -0.08333333333 Combine like terms: 0 + -0.08333333333 = -0.08333333333 -1x + x2 = -0.08333333333 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = -0.08333333333 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.08333333333 + 0.25 Combine like terms: -0.08333333333 + 0.25 = 0.16666666667 0.25 + -1x + x2 = 0.16666666667 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.16666666667 Calculate the square root of the right side: 0.40824829 Break this problem into two subproblems by setting (x + -0.5) equal to 0.40824829 and -0.40824829.Subproblem 1
x + -0.5 = 0.40824829 Simplifying x + -0.5 = 0.40824829 Reorder the terms: -0.5 + x = 0.40824829 Solving -0.5 + x = 0.40824829 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.40824829 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.40824829 + 0.5 x = 0.40824829 + 0.5 Combine like terms: 0.40824829 + 0.5 = 0.90824829 x = 0.90824829 Simplifying x = 0.90824829Subproblem 2
x + -0.5 = -0.40824829 Simplifying x + -0.5 = -0.40824829 Reorder the terms: -0.5 + x = -0.40824829 Solving -0.5 + x = -0.40824829 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.40824829 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.40824829 + 0.5 x = -0.40824829 + 0.5 Combine like terms: -0.40824829 + 0.5 = 0.09175171 x = 0.09175171 Simplifying x = 0.09175171Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.90824829, 0.09175171}
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