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Simplifying (0.5x2) + -6x + 8 = 0 Reorder the terms: 8 + -6x + (0.5x2) = 0 Solving 8 + -6x + (0.5x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 16 + -12x + x2 = 0 Move the constant term to the right: Add '-16' to each side of the equation. 16 + -12x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + -12x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -12x + x2 = 0 + -16 -12x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 -12x + x2 = -16 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 = -16 + 36 Reorder the terms: 36 + -12x + x2 = -16 + 36 Combine like terms: -16 + 36 = 20 36 + -12x + x2 = 20 Factor a perfect square on the left side: ((x) + -6)((x) + -6) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting ((x) + -6) equal to 4.472135955 and -4.472135955.Subproblem 1
(x) + -6 = 4.472135955 Simplifying (x) + -6 = 4.472135955 x + -6 = 4.472135955 Reorder the terms: -6 + x = 4.472135955 Solving -6 + x = 4.472135955 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 = 4.472135955 + 6 Combine like terms: -6 + 6 = 0 0 + x = 4.472135955 + 6 x = 4.472135955 + 6 Combine like terms: 4.472135955 + 6 = 10.472135955 x = 10.472135955 Simplifying x = 10.472135955Subproblem 2
(x) + -6 = -4.472135955 Simplifying (x) + -6 = -4.472135955 x + -6 = -4.472135955 Reorder the terms: -6 + x = -4.472135955 Solving -6 + x = -4.472135955 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 = -4.472135955 + 6 Combine like terms: -6 + 6 = 0 0 + x = -4.472135955 + 6 x = -4.472135955 + 6 Combine like terms: -4.472135955 + 6 = 1.527864045 x = 1.527864045 Simplifying x = 1.527864045Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.472135955, 1.527864045}
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