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Simplifying 6x2 = 12x + -1.8 Reorder the terms: 6x2 = -1.8 + 12x Solving 6x2 = -1.8 + 12x Solving for variable 'x'. Reorder the terms: 1.8 + -12x + 6x2 = -1.8 + 12x + 1.8 + -12x Reorder the terms: 1.8 + -12x + 6x2 = -1.8 + 1.8 + 12x + -12x Combine like terms: -1.8 + 1.8 = 0.0 1.8 + -12x + 6x2 = 0.0 + 12x + -12x 1.8 + -12x + 6x2 = 12x + -12x Combine like terms: 12x + -12x = 0 1.8 + -12x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.3 + -2x + x2 = 0 Move the constant term to the right: Add '-0.3' to each side of the equation. 0.3 + -2x + -0.3 + x2 = 0 + -0.3 Reorder the terms: 0.3 + -0.3 + -2x + x2 = 0 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + -2x + x2 = 0 + -0.3 -2x + x2 = 0 + -0.3 Combine like terms: 0 + -0.3 = -0.3 -2x + x2 = -0.3 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -0.3 + 1 Reorder the terms: 1 + -2x + x2 = -0.3 + 1 Combine like terms: -0.3 + 1 = 0.7 1 + -2x + x2 = 0.7 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.7 Calculate the square root of the right side: 0.836660027 Break this problem into two subproblems by setting (x + -1) equal to 0.836660027 and -0.836660027.Subproblem 1
x + -1 = 0.836660027 Simplifying x + -1 = 0.836660027 Reorder the terms: -1 + x = 0.836660027 Solving -1 + x = 0.836660027 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0.836660027 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.836660027 + 1 x = 0.836660027 + 1 Combine like terms: 0.836660027 + 1 = 1.836660027 x = 1.836660027 Simplifying x = 1.836660027Subproblem 2
x + -1 = -0.836660027 Simplifying x + -1 = -0.836660027 Reorder the terms: -1 + x = -0.836660027 Solving -1 + x = -0.836660027 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -0.836660027 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.836660027 + 1 x = -0.836660027 + 1 Combine like terms: -0.836660027 + 1 = 0.163339973 x = 0.163339973 Simplifying x = 0.163339973Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.836660027, 0.163339973}
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