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Simplifying 5x2 + -12x + -227 = 0 Reorder the terms: -227 + -12x + 5x2 = 0 Solving -227 + -12x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -45.4 + -2.4x + x2 = 0 Move the constant term to the right: Add '45.4' to each side of the equation. -45.4 + -2.4x + 45.4 + x2 = 0 + 45.4 Reorder the terms: -45.4 + 45.4 + -2.4x + x2 = 0 + 45.4 Combine like terms: -45.4 + 45.4 = 0.0 0.0 + -2.4x + x2 = 0 + 45.4 -2.4x + x2 = 0 + 45.4 Combine like terms: 0 + 45.4 = 45.4 -2.4x + x2 = 45.4 The x term is -2.4x. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4x + 1.44 + x2 = 45.4 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = 45.4 + 1.44 Combine like terms: 45.4 + 1.44 = 46.84 1.44 + -2.4x + x2 = 46.84 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 46.84 Calculate the square root of the right side: 6.843975453 Break this problem into two subproblems by setting (x + -1.2) equal to 6.843975453 and -6.843975453.Subproblem 1
x + -1.2 = 6.843975453 Simplifying x + -1.2 = 6.843975453 Reorder the terms: -1.2 + x = 6.843975453 Solving -1.2 + x = 6.843975453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 6.843975453 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 6.843975453 + 1.2 x = 6.843975453 + 1.2 Combine like terms: 6.843975453 + 1.2 = 8.043975453 x = 8.043975453 Simplifying x = 8.043975453Subproblem 2
x + -1.2 = -6.843975453 Simplifying x + -1.2 = -6.843975453 Reorder the terms: -1.2 + x = -6.843975453 Solving -1.2 + x = -6.843975453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -6.843975453 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -6.843975453 + 1.2 x = -6.843975453 + 1.2 Combine like terms: -6.843975453 + 1.2 = -5.643975453 x = -5.643975453 Simplifying x = -5.643975453Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.043975453, -5.643975453}
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