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Simplifying 4x2 + -1x + -40 = 0 Reorder the terms: -40 + -1x + 4x2 = 0 Solving -40 + -1x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -10 + -0.25x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -0.25x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -0.25x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -0.25x + x2 = 0 + 10 -0.25x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -0.25x + x2 = 10 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 10 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 10 + 0.015625 Combine like terms: 10 + 0.015625 = 10.015625 0.015625 + -0.25x + x2 = 10.015625 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 10.015625 Calculate the square root of the right side: 3.164747225 Break this problem into two subproblems by setting (x + -0.125) equal to 3.164747225 and -3.164747225.Subproblem 1
x + -0.125 = 3.164747225 Simplifying x + -0.125 = 3.164747225 Reorder the terms: -0.125 + x = 3.164747225 Solving -0.125 + x = 3.164747225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 3.164747225 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 3.164747225 + 0.125 x = 3.164747225 + 0.125 Combine like terms: 3.164747225 + 0.125 = 3.289747225 x = 3.289747225 Simplifying x = 3.289747225Subproblem 2
x + -0.125 = -3.164747225 Simplifying x + -0.125 = -3.164747225 Reorder the terms: -0.125 + x = -3.164747225 Solving -0.125 + x = -3.164747225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -3.164747225 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -3.164747225 + 0.125 x = -3.164747225 + 0.125 Combine like terms: -3.164747225 + 0.125 = -3.039747225 x = -3.039747225 Simplifying x = -3.039747225Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.289747225, -3.039747225}
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