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Simplifying 0.3x2 + -3.45x + 3 = 0 Reorder the terms: 3 + -3.45x + 0.3x2 = 0 Solving 3 + -3.45x + 0.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.3 the coefficient of the squared term: Divide each side by '0.3'. 10 + -11.5x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -11.5x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -11.5x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -11.5x + x2 = 0 + -10 -11.5x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -11.5x + x2 = -10 The x term is -11.5x. Take half its coefficient (-5.75). Square it (33.0625) and add it to both sides. Add '33.0625' to each side of the equation. -11.5x + 33.0625 + x2 = -10 + 33.0625 Reorder the terms: 33.0625 + -11.5x + x2 = -10 + 33.0625 Combine like terms: -10 + 33.0625 = 23.0625 33.0625 + -11.5x + x2 = 23.0625 Factor a perfect square on the left side: (x + -5.75)(x + -5.75) = 23.0625 Calculate the square root of the right side: 4.802343178 Break this problem into two subproblems by setting (x + -5.75) equal to 4.802343178 and -4.802343178.Subproblem 1
x + -5.75 = 4.802343178 Simplifying x + -5.75 = 4.802343178 Reorder the terms: -5.75 + x = 4.802343178 Solving -5.75 + x = 4.802343178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + x = 4.802343178 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + x = 4.802343178 + 5.75 x = 4.802343178 + 5.75 Combine like terms: 4.802343178 + 5.75 = 10.552343178 x = 10.552343178 Simplifying x = 10.552343178Subproblem 2
x + -5.75 = -4.802343178 Simplifying x + -5.75 = -4.802343178 Reorder the terms: -5.75 + x = -4.802343178 Solving -5.75 + x = -4.802343178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + x = -4.802343178 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + x = -4.802343178 + 5.75 x = -4.802343178 + 5.75 Combine like terms: -4.802343178 + 5.75 = 0.947656822 x = 0.947656822 Simplifying x = 0.947656822Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.552343178, 0.947656822}
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