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Simplifying 5x2 + 42x + 32 = 0 Reorder the terms: 32 + 42x + 5x2 = 0 Solving 32 + 42x + 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'. 6.4 + 8.4x + x2 = 0 Move the constant term to the right: Add '-6.4' to each side of the equation. 6.4 + 8.4x + -6.4 + x2 = 0 + -6.4 Reorder the terms: 6.4 + -6.4 + 8.4x + x2 = 0 + -6.4 Combine like terms: 6.4 + -6.4 = 0.0 0.0 + 8.4x + x2 = 0 + -6.4 8.4x + x2 = 0 + -6.4 Combine like terms: 0 + -6.4 = -6.4 8.4x + x2 = -6.4 The x term is 8.4x. Take half its coefficient (4.2). Square it (17.64) and add it to both sides. Add '17.64' to each side of the equation. 8.4x + 17.64 + x2 = -6.4 + 17.64 Reorder the terms: 17.64 + 8.4x + x2 = -6.4 + 17.64 Combine like terms: -6.4 + 17.64 = 11.24 17.64 + 8.4x + x2 = 11.24 Factor a perfect square on the left side: (x + 4.2)(x + 4.2) = 11.24 Calculate the square root of the right side: 3.352610923 Break this problem into two subproblems by setting (x + 4.2) equal to 3.352610923 and -3.352610923.Subproblem 1
x + 4.2 = 3.352610923 Simplifying x + 4.2 = 3.352610923 Reorder the terms: 4.2 + x = 3.352610923 Solving 4.2 + x = 3.352610923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.2' to each side of the equation. 4.2 + -4.2 + x = 3.352610923 + -4.2 Combine like terms: 4.2 + -4.2 = 0.0 0.0 + x = 3.352610923 + -4.2 x = 3.352610923 + -4.2 Combine like terms: 3.352610923 + -4.2 = -0.847389077 x = -0.847389077 Simplifying x = -0.847389077Subproblem 2
x + 4.2 = -3.352610923 Simplifying x + 4.2 = -3.352610923 Reorder the terms: 4.2 + x = -3.352610923 Solving 4.2 + x = -3.352610923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.2' to each side of the equation. 4.2 + -4.2 + x = -3.352610923 + -4.2 Combine like terms: 4.2 + -4.2 = 0.0 0.0 + x = -3.352610923 + -4.2 x = -3.352610923 + -4.2 Combine like terms: -3.352610923 + -4.2 = -7.552610923 x = -7.552610923 Simplifying x = -7.552610923Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.847389077, -7.552610923}
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