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Simplifying 5x2 + -1x = 3x + 2 Reorder the terms: -1x + 5x2 = 3x + 2 Reorder the terms: -1x + 5x2 = 2 + 3x Solving -1x + 5x2 = 2 + 3x Solving for variable 'x'. Reorder the terms: -2 + -1x + -3x + 5x2 = 2 + 3x + -2 + -3x Combine like terms: -1x + -3x = -4x -2 + -4x + 5x2 = 2 + 3x + -2 + -3x Reorder the terms: -2 + -4x + 5x2 = 2 + -2 + 3x + -3x Combine like terms: 2 + -2 = 0 -2 + -4x + 5x2 = 0 + 3x + -3x -2 + -4x + 5x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -2 + -4x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + -0.8x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -0.8x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -0.8x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -0.8x + x2 = 0 + 0.4 -0.8x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -0.8x + x2 = 0.4 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 = 0.4 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 0.4 + 0.16 Combine like terms: 0.4 + 0.16 = 0.56 0.16 + -0.8x + x2 = 0.56 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 0.56 Calculate the square root of the right side: 0.748331477 Break this problem into two subproblems by setting (x + -0.4) equal to 0.748331477 and -0.748331477.Subproblem 1
x + -0.4 = 0.748331477 Simplifying x + -0.4 = 0.748331477 Reorder the terms: -0.4 + x = 0.748331477 Solving -0.4 + x = 0.748331477 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 = 0.748331477 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 0.748331477 + 0.4 x = 0.748331477 + 0.4 Combine like terms: 0.748331477 + 0.4 = 1.148331477 x = 1.148331477 Simplifying x = 1.148331477Subproblem 2
x + -0.4 = -0.748331477 Simplifying x + -0.4 = -0.748331477 Reorder the terms: -0.4 + x = -0.748331477 Solving -0.4 + x = -0.748331477 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 = -0.748331477 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -0.748331477 + 0.4 x = -0.748331477 + 0.4 Combine like terms: -0.748331477 + 0.4 = -0.348331477 x = -0.348331477 Simplifying x = -0.348331477Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.148331477, -0.348331477}
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