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Simplifying (5x2 + -2x + -5x3 + 3) + -1(2x + -6x + -5x3 + 5) = 0 Reorder the terms: (3 + -2x + 5x2 + -5x3) + -1(2x + -6x + -5x3 + 5) = 0 Remove parenthesis around (3 + -2x + 5x2 + -5x3) 3 + -2x + 5x2 + -5x3 + -1(2x + -6x + -5x3 + 5) = 0 Reorder the terms: 3 + -2x + 5x2 + -5x3 + -1(5 + 2x + -6x + -5x3) = 0 Combine like terms: 2x + -6x = -4x 3 + -2x + 5x2 + -5x3 + -1(5 + -4x + -5x3) = 0 3 + -2x + 5x2 + -5x3 + (5 * -1 + -4x * -1 + -5x3 * -1) = 0 3 + -2x + 5x2 + -5x3 + (-5 + 4x + 5x3) = 0 Reorder the terms: 3 + -5 + -2x + 4x + 5x2 + -5x3 + 5x3 = 0 Combine like terms: 3 + -5 = -2 -2 + -2x + 4x + 5x2 + -5x3 + 5x3 = 0 Combine like terms: -2x + 4x = 2x -2 + 2x + 5x2 + -5x3 + 5x3 = 0 Combine like terms: -5x3 + 5x3 = 0 -2 + 2x + 5x2 + 0 = 0 -2 + 2x + 5x2 = 0 Solving -2 + 2x + 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'. -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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