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Simplifying -5x2 + -12x + 18 = 0 Reorder the terms: 18 + -12x + -5x2 = 0 Solving 18 + -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'. -3.6 + 2.4x + x2 = 0 Move the constant term to the right: Add '3.6' to each side of the equation. -3.6 + 2.4x + 3.6 + x2 = 0 + 3.6 Reorder the terms: -3.6 + 3.6 + 2.4x + x2 = 0 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + 2.4x + x2 = 0 + 3.6 2.4x + x2 = 0 + 3.6 Combine like terms: 0 + 3.6 = 3.6 2.4x + x2 = 3.6 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 = 3.6 + 1.44 Reorder the terms: 1.44 + 2.4x + x2 = 3.6 + 1.44 Combine like terms: 3.6 + 1.44 = 5.04 1.44 + 2.4x + x2 = 5.04 Factor a perfect square on the left side: (x + 1.2)(x + 1.2) = 5.04 Calculate the square root of the right side: 2.244994432 Break this problem into two subproblems by setting (x + 1.2) equal to 2.244994432 and -2.244994432.Subproblem 1
x + 1.2 = 2.244994432 Simplifying x + 1.2 = 2.244994432 Reorder the terms: 1.2 + x = 2.244994432 Solving 1.2 + x = 2.244994432 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 = 2.244994432 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = 2.244994432 + -1.2 x = 2.244994432 + -1.2 Combine like terms: 2.244994432 + -1.2 = 1.044994432 x = 1.044994432 Simplifying x = 1.044994432Subproblem 2
x + 1.2 = -2.244994432 Simplifying x + 1.2 = -2.244994432 Reorder the terms: 1.2 + x = -2.244994432 Solving 1.2 + x = -2.244994432 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 = -2.244994432 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = -2.244994432 + -1.2 x = -2.244994432 + -1.2 Combine like terms: -2.244994432 + -1.2 = -3.444994432 x = -3.444994432 Simplifying x = -3.444994432Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.044994432, -3.444994432}
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