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Simplifying 1.45 = 1 + 3x + 3x2 Solving 1.45 = 1 + 3x + 3x2 Solving for variable 'x'. Combine like terms: 1.45 + -1 = 0.45 0.45 + -3x + -3x2 = 1 + 3x + 3x2 + -1 + -3x + -3x2 Reorder the terms: 0.45 + -3x + -3x2 = 1 + -1 + 3x + -3x + 3x2 + -3x2 Combine like terms: 1 + -1 = 0 0.45 + -3x + -3x2 = 0 + 3x + -3x + 3x2 + -3x2 0.45 + -3x + -3x2 = 3x + -3x + 3x2 + -3x2 Combine like terms: 3x + -3x = 0 0.45 + -3x + -3x2 = 0 + 3x2 + -3x2 0.45 + -3x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 0.45 + -3x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -0.15 + x + x2 = 0 Move the constant term to the right: Add '0.15' to each side of the equation. -0.15 + x + 0.15 + x2 = 0 + 0.15 Reorder the terms: -0.15 + 0.15 + x + x2 = 0 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x + x2 = 0 + 0.15 x + x2 = 0 + 0.15 Combine like terms: 0 + 0.15 = 0.15 x + x2 = 0.15 The x term is x. 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. + 0.25 + x2 = 0.15 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 0.15 + 0.25 Combine like terms: 0.15 + 0.25 = 0.4 1.25 + x2 = 0.4 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.4 Calculate the square root of the right side: 0.632455532 Break this problem into two subproblems by setting (x + 0.5) equal to 0.632455532 and -0.632455532.Subproblem 1
x + 0.5 = 0.632455532 Simplifying x + 0.5 = 0.632455532 Reorder the terms: 0.5 + x = 0.632455532 Solving 0.5 + x = 0.632455532 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 = 0.632455532 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.632455532 + -0.5 x = 0.632455532 + -0.5 Combine like terms: 0.632455532 + -0.5 = 0.132455532 x = 0.132455532 Simplifying x = 0.132455532Subproblem 2
x + 0.5 = -0.632455532 Simplifying x + 0.5 = -0.632455532 Reorder the terms: 0.5 + x = -0.632455532 Solving 0.5 + x = -0.632455532 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 = -0.632455532 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.632455532 + -0.5 x = -0.632455532 + -0.5 Combine like terms: -0.632455532 + -0.5 = -1.132455532 x = -1.132455532 Simplifying x = -1.132455532Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.132455532, -1.132455532}
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