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Simplifying x2 + 8.4x + -40 = 0 Reorder the terms: -40 + 8.4x + x2 = 0 Solving -40 + 8.4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + 8.4x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + 8.4x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 8.4x + x2 = 0 + 40 8.4x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 8.4x + x2 = 40 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 = 40 + 17.64 Reorder the terms: 17.64 + 8.4x + x2 = 40 + 17.64 Combine like terms: 40 + 17.64 = 57.64 17.64 + 8.4x + x2 = 57.64 Factor a perfect square on the left side: (x + 4.2)(x + 4.2) = 57.64 Calculate the square root of the right side: 7.592101158 Break this problem into two subproblems by setting (x + 4.2) equal to 7.592101158 and -7.592101158.Subproblem 1
x + 4.2 = 7.592101158 Simplifying x + 4.2 = 7.592101158 Reorder the terms: 4.2 + x = 7.592101158 Solving 4.2 + x = 7.592101158 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 = 7.592101158 + -4.2 Combine like terms: 4.2 + -4.2 = 0.0 0.0 + x = 7.592101158 + -4.2 x = 7.592101158 + -4.2 Combine like terms: 7.592101158 + -4.2 = 3.392101158 x = 3.392101158 Simplifying x = 3.392101158Subproblem 2
x + 4.2 = -7.592101158 Simplifying x + 4.2 = -7.592101158 Reorder the terms: 4.2 + x = -7.592101158 Solving 4.2 + x = -7.592101158 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 = -7.592101158 + -4.2 Combine like terms: 4.2 + -4.2 = 0.0 0.0 + x = -7.592101158 + -4.2 x = -7.592101158 + -4.2 Combine like terms: -7.592101158 + -4.2 = -11.792101158 x = -11.792101158 Simplifying x = -11.792101158Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.392101158, -11.792101158}
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