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Simplifying 5x2 + 12x + -27 = 0 Reorder the terms: -27 + 12x + 5x2 = 0 Solving -27 + 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'. -5.4 + 2.4x + x2 = 0 Move the constant term to the right: Add '5.4' to each side of the equation. -5.4 + 2.4x + 5.4 + x2 = 0 + 5.4 Reorder the terms: -5.4 + 5.4 + 2.4x + x2 = 0 + 5.4 Combine like terms: -5.4 + 5.4 = 0.0 0.0 + 2.4x + x2 = 0 + 5.4 2.4x + x2 = 0 + 5.4 Combine like terms: 0 + 5.4 = 5.4 2.4x + x2 = 5.4 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 = 5.4 + 1.44 Reorder the terms: 1.44 + 2.4x + x2 = 5.4 + 1.44 Combine like terms: 5.4 + 1.44 = 6.84 1.44 + 2.4x + x2 = 6.84 Factor a perfect square on the left side: (x + 1.2)(x + 1.2) = 6.84 Calculate the square root of the right side: 2.615339366 Break this problem into two subproblems by setting (x + 1.2) equal to 2.615339366 and -2.615339366.Subproblem 1
x + 1.2 = 2.615339366 Simplifying x + 1.2 = 2.615339366 Reorder the terms: 1.2 + x = 2.615339366 Solving 1.2 + x = 2.615339366 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 = 2.615339366 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = 2.615339366 + -1.2 x = 2.615339366 + -1.2 Combine like terms: 2.615339366 + -1.2 = 1.415339366 x = 1.415339366 Simplifying x = 1.415339366Subproblem 2
x + 1.2 = -2.615339366 Simplifying x + 1.2 = -2.615339366 Reorder the terms: 1.2 + x = -2.615339366 Solving 1.2 + x = -2.615339366 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 = -2.615339366 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = -2.615339366 + -1.2 x = -2.615339366 + -1.2 Combine like terms: -2.615339366 + -1.2 = -3.815339366 x = -3.815339366 Simplifying x = -3.815339366Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.415339366, -3.815339366}
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