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Simplifying 3x2 + 5x + 6 = 3x + 8 + -2x2 Reorder the terms: 6 + 5x + 3x2 = 3x + 8 + -2x2 Reorder the terms: 6 + 5x + 3x2 = 8 + 3x + -2x2 Solving 6 + 5x + 3x2 = 8 + 3x + -2x2 Solving for variable 'x'. Reorder the terms: 6 + -8 + 5x + -3x + 3x2 + 2x2 = 8 + 3x + -2x2 + -8 + -3x + 2x2 Combine like terms: 6 + -8 = -2 -2 + 5x + -3x + 3x2 + 2x2 = 8 + 3x + -2x2 + -8 + -3x + 2x2 Combine like terms: 5x + -3x = 2x -2 + 2x + 3x2 + 2x2 = 8 + 3x + -2x2 + -8 + -3x + 2x2 Combine like terms: 3x2 + 2x2 = 5x2 -2 + 2x + 5x2 = 8 + 3x + -2x2 + -8 + -3x + 2x2 Reorder the terms: -2 + 2x + 5x2 = 8 + -8 + 3x + -3x + -2x2 + 2x2 Combine like terms: 8 + -8 = 0 -2 + 2x + 5x2 = 0 + 3x + -3x + -2x2 + 2x2 -2 + 2x + 5x2 = 3x + -3x + -2x2 + 2x2 Combine like terms: 3x + -3x = 0 -2 + 2x + 5x2 = 0 + -2x2 + 2x2 -2 + 2x + 5x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -2 + 2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + 0.4x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 0.4x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 0.4x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 0.4x + x2 = 0 + 0.4 0.4x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 0.4x + x2 = 0.4 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 0.4 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 0.4 + 0.04 Combine like terms: 0.4 + 0.04 = 0.44 0.04 + 0.4x + x2 = 0.44 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 0.44 Calculate the square root of the right side: 0.663324958 Break this problem into two subproblems by setting (x + 0.2) equal to 0.663324958 and -0.663324958.Subproblem 1
x + 0.2 = 0.663324958 Simplifying x + 0.2 = 0.663324958 Reorder the terms: 0.2 + x = 0.663324958 Solving 0.2 + x = 0.663324958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 0.663324958 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 0.663324958 + -0.2 x = 0.663324958 + -0.2 Combine like terms: 0.663324958 + -0.2 = 0.463324958 x = 0.463324958 Simplifying x = 0.463324958Subproblem 2
x + 0.2 = -0.663324958 Simplifying x + 0.2 = -0.663324958 Reorder the terms: 0.2 + x = -0.663324958 Solving 0.2 + x = -0.663324958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -0.663324958 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -0.663324958 + -0.2 x = -0.663324958 + -0.2 Combine like terms: -0.663324958 + -0.2 = -0.863324958 x = -0.863324958 Simplifying x = -0.863324958Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.463324958, -0.863324958}
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