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Simplifying 10x2 + 40x + 31 = 0 Reorder the terms: 31 + 40x + 10x2 = 0 Solving 31 + 40x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 3.1 + 4x + x2 = 0 Move the constant term to the right: Add '-3.1' to each side of the equation. 3.1 + 4x + -3.1 + x2 = 0 + -3.1 Reorder the terms: 3.1 + -3.1 + 4x + x2 = 0 + -3.1 Combine like terms: 3.1 + -3.1 = 0.0 0.0 + 4x + x2 = 0 + -3.1 4x + x2 = 0 + -3.1 Combine like terms: 0 + -3.1 = -3.1 4x + x2 = -3.1 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -3.1 + 4 Reorder the terms: 4 + 4x + x2 = -3.1 + 4 Combine like terms: -3.1 + 4 = 0.9 4 + 4x + x2 = 0.9 Factor a perfect square on the left side: (x + 2)(x + 2) = 0.9 Calculate the square root of the right side: 0.948683298 Break this problem into two subproblems by setting (x + 2) equal to 0.948683298 and -0.948683298.Subproblem 1
x + 2 = 0.948683298 Simplifying x + 2 = 0.948683298 Reorder the terms: 2 + x = 0.948683298 Solving 2 + x = 0.948683298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0.948683298 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0.948683298 + -2 x = 0.948683298 + -2 Combine like terms: 0.948683298 + -2 = -1.051316702 x = -1.051316702 Simplifying x = -1.051316702Subproblem 2
x + 2 = -0.948683298 Simplifying x + 2 = -0.948683298 Reorder the terms: 2 + x = -0.948683298 Solving 2 + x = -0.948683298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -0.948683298 + -2 Combine like terms: 2 + -2 = 0 0 + x = -0.948683298 + -2 x = -0.948683298 + -2 Combine like terms: -0.948683298 + -2 = -2.948683298 x = -2.948683298 Simplifying x = -2.948683298Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.051316702, -2.948683298}
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