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Simplifying 3x2 + 2x2 = 12x + 18 Combine like terms: 3x2 + 2x2 = 5x2 5x2 = 12x + 18 Reorder the terms: 5x2 = 18 + 12x Solving 5x2 = 18 + 12x Solving for variable 'x'. Reorder the terms: -18 + -12x + 5x2 = 18 + 12x + -18 + -12x Reorder the terms: -18 + -12x + 5x2 = 18 + -18 + 12x + -12x Combine like terms: 18 + -18 = 0 -18 + -12x + 5x2 = 0 + 12x + -12x -18 + -12x + 5x2 = 12x + -12x Combine like terms: 12x + -12x = 0 -18 + -12x + 5x2 = 0 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 = 3.444994432 x = 3.444994432 Simplifying x = 3.444994432Subproblem 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 = -1.044994432 x = -1.044994432 Simplifying x = -1.044994432Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.444994432, -1.044994432}
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