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Simplifying 5x2 + 31x + 46 = 0 Reorder the terms: 46 + 31x + 5x2 = 0 Solving 46 + 31x + 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'. 9.2 + 6.2x + x2 = 0 Move the constant term to the right: Add '-9.2' to each side of the equation. 9.2 + 6.2x + -9.2 + x2 = 0 + -9.2 Reorder the terms: 9.2 + -9.2 + 6.2x + x2 = 0 + -9.2 Combine like terms: 9.2 + -9.2 = 0.0 0.0 + 6.2x + x2 = 0 + -9.2 6.2x + x2 = 0 + -9.2 Combine like terms: 0 + -9.2 = -9.2 6.2x + x2 = -9.2 The x term is 6.2x. Take half its coefficient (3.1). Square it (9.61) and add it to both sides. Add '9.61' to each side of the equation. 6.2x + 9.61 + x2 = -9.2 + 9.61 Reorder the terms: 9.61 + 6.2x + x2 = -9.2 + 9.61 Combine like terms: -9.2 + 9.61 = 0.41 9.61 + 6.2x + x2 = 0.41 Factor a perfect square on the left side: (x + 3.1)(x + 3.1) = 0.41 Calculate the square root of the right side: 0.640312424 Break this problem into two subproblems by setting (x + 3.1) equal to 0.640312424 and -0.640312424.Subproblem 1
x + 3.1 = 0.640312424 Simplifying x + 3.1 = 0.640312424 Reorder the terms: 3.1 + x = 0.640312424 Solving 3.1 + x = 0.640312424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.1' to each side of the equation. 3.1 + -3.1 + x = 0.640312424 + -3.1 Combine like terms: 3.1 + -3.1 = 0.0 0.0 + x = 0.640312424 + -3.1 x = 0.640312424 + -3.1 Combine like terms: 0.640312424 + -3.1 = -2.459687576 x = -2.459687576 Simplifying x = -2.459687576Subproblem 2
x + 3.1 = -0.640312424 Simplifying x + 3.1 = -0.640312424 Reorder the terms: 3.1 + x = -0.640312424 Solving 3.1 + x = -0.640312424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.1' to each side of the equation. 3.1 + -3.1 + x = -0.640312424 + -3.1 Combine like terms: 3.1 + -3.1 = 0.0 0.0 + x = -0.640312424 + -3.1 x = -0.640312424 + -3.1 Combine like terms: -0.640312424 + -3.1 = -3.740312424 x = -3.740312424 Simplifying x = -3.740312424Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.459687576, -3.740312424}
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