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Simplifying (5x2 + -2x) + (6x + -4) = 0 Reorder the terms: (-2x + 5x2) + (6x + -4) = 0 Remove parenthesis around (-2x + 5x2) -2x + 5x2 + (6x + -4) = 0 Reorder the terms: -2x + 5x2 + (-4 + 6x) = 0 Remove parenthesis around (-4 + 6x) -2x + 5x2 + -4 + 6x = 0 Reorder the terms: -4 + -2x + 6x + 5x2 = 0 Combine like terms: -2x + 6x = 4x -4 + 4x + 5x2 = 0 Solving -4 + 4x + 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'. -0.8 + 0.8x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 0.8x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + 0.8x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 0.8x + x2 = 0 + 0.8 0.8x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 0.8x + x2 = 0.8 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = 0.8 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 0.8 + 0.16 Combine like terms: 0.8 + 0.16 = 0.96 0.16 + 0.8x + x2 = 0.96 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 0.96 Calculate the square root of the right side: 0.979795897 Break this problem into two subproblems by setting (x + 0.4) equal to 0.979795897 and -0.979795897.Subproblem 1
x + 0.4 = 0.979795897 Simplifying x + 0.4 = 0.979795897 Reorder the terms: 0.4 + x = 0.979795897 Solving 0.4 + x = 0.979795897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 0.979795897 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 0.979795897 + -0.4 x = 0.979795897 + -0.4 Combine like terms: 0.979795897 + -0.4 = 0.579795897 x = 0.579795897 Simplifying x = 0.579795897Subproblem 2
x + 0.4 = -0.979795897 Simplifying x + 0.4 = -0.979795897 Reorder the terms: 0.4 + x = -0.979795897 Solving 0.4 + x = -0.979795897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -0.979795897 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -0.979795897 + -0.4 x = -0.979795897 + -0.4 Combine like terms: -0.979795897 + -0.4 = -1.379795897 x = -1.379795897 Simplifying x = -1.379795897Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.579795897, -1.379795897}
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