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Simplifying 3x2 + -36x + 100 = 0 Reorder the terms: 100 + -36x + 3x2 = 0 Solving 100 + -36x + 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'. 33.33333333 + -12x + x2 = 0 Move the constant term to the right: Add '-33.33333333' to each side of the equation. 33.33333333 + -12x + -33.33333333 + x2 = 0 + -33.33333333 Reorder the terms: 33.33333333 + -33.33333333 + -12x + x2 = 0 + -33.33333333 Combine like terms: 33.33333333 + -33.33333333 = 0.00000000 0.00000000 + -12x + x2 = 0 + -33.33333333 -12x + x2 = 0 + -33.33333333 Combine like terms: 0 + -33.33333333 = -33.33333333 -12x + x2 = -33.33333333 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 = -33.33333333 + 36 Reorder the terms: 36 + -12x + x2 = -33.33333333 + 36 Combine like terms: -33.33333333 + 36 = 2.66666667 36 + -12x + x2 = 2.66666667 Factor a perfect square on the left side: (x + -6)(x + -6) = 2.66666667 Calculate the square root of the right side: 1.632993163 Break this problem into two subproblems by setting (x + -6) equal to 1.632993163 and -1.632993163.Subproblem 1
x + -6 = 1.632993163 Simplifying x + -6 = 1.632993163 Reorder the terms: -6 + x = 1.632993163 Solving -6 + x = 1.632993163 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 = 1.632993163 + 6 Combine like terms: -6 + 6 = 0 0 + x = 1.632993163 + 6 x = 1.632993163 + 6 Combine like terms: 1.632993163 + 6 = 7.632993163 x = 7.632993163 Simplifying x = 7.632993163Subproblem 2
x + -6 = -1.632993163 Simplifying x + -6 = -1.632993163 Reorder the terms: -6 + x = -1.632993163 Solving -6 + x = -1.632993163 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 = -1.632993163 + 6 Combine like terms: -6 + 6 = 0 0 + x = -1.632993163 + 6 x = -1.632993163 + 6 Combine like terms: -1.632993163 + 6 = 4.367006837 x = 4.367006837 Simplifying x = 4.367006837Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.632993163, 4.367006837}
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