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Simplifying (3x2) + -30x + 62 = 0 Reorder the terms: 62 + -30x + (3x2) = 0 Solving 62 + -30x + (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'. 20.66666667 + -10x + x2 = 0 Move the constant term to the right: Add '-20.66666667' to each side of the equation. 20.66666667 + -10x + -20.66666667 + x2 = 0 + -20.66666667 Reorder the terms: 20.66666667 + -20.66666667 + -10x + x2 = 0 + -20.66666667 Combine like terms: 20.66666667 + -20.66666667 = 0.00000000 0.00000000 + -10x + x2 = 0 + -20.66666667 -10x + x2 = 0 + -20.66666667 Combine like terms: 0 + -20.66666667 = -20.66666667 -10x + x2 = -20.66666667 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -20.66666667 + 25 Reorder the terms: 25 + -10x + x2 = -20.66666667 + 25 Combine like terms: -20.66666667 + 25 = 4.33333333 25 + -10x + x2 = 4.33333333 Factor a perfect square on the left side: ((x) + -5)((x) + -5) = 4.33333333 Calculate the square root of the right side: 2.081665999 Break this problem into two subproblems by setting ((x) + -5) equal to 2.081665999 and -2.081665999.Subproblem 1
(x) + -5 = 2.081665999 Simplifying (x) + -5 = 2.081665999 x + -5 = 2.081665999 Reorder the terms: -5 + x = 2.081665999 Solving -5 + x = 2.081665999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 2.081665999 + 5 Combine like terms: -5 + 5 = 0 0 + x = 2.081665999 + 5 x = 2.081665999 + 5 Combine like terms: 2.081665999 + 5 = 7.081665999 x = 7.081665999 Simplifying x = 7.081665999Subproblem 2
(x) + -5 = -2.081665999 Simplifying (x) + -5 = -2.081665999 x + -5 = -2.081665999 Reorder the terms: -5 + x = -2.081665999 Solving -5 + x = -2.081665999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -2.081665999 + 5 Combine like terms: -5 + 5 = 0 0 + x = -2.081665999 + 5 x = -2.081665999 + 5 Combine like terms: -2.081665999 + 5 = 2.918334001 x = 2.918334001 Simplifying x = 2.918334001Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.081665999, 2.918334001}
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