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Simplifying 2x2 + 14x + 21.5 = 0 Reorder the terms: 21.5 + 14x + 2x2 = 0 Solving 21.5 + 14x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 10.75 + 7x + x2 = 0 Move the constant term to the right: Add '-10.75' to each side of the equation. 10.75 + 7x + -10.75 + x2 = 0 + -10.75 Reorder the terms: 10.75 + -10.75 + 7x + x2 = 0 + -10.75 Combine like terms: 10.75 + -10.75 = 0.00 0.00 + 7x + x2 = 0 + -10.75 7x + x2 = 0 + -10.75 Combine like terms: 0 + -10.75 = -10.75 7x + x2 = -10.75 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -10.75 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -10.75 + 12.25 Combine like terms: -10.75 + 12.25 = 1.5 12.25 + 7x + x2 = 1.5 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (x + 3.5) equal to 1.224744871 and -1.224744871.Subproblem 1
x + 3.5 = 1.224744871 Simplifying x + 3.5 = 1.224744871 Reorder the terms: 3.5 + x = 1.224744871 Solving 3.5 + x = 1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 1.224744871 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 1.224744871 + -3.5 x = 1.224744871 + -3.5 Combine like terms: 1.224744871 + -3.5 = -2.275255129 x = -2.275255129 Simplifying x = -2.275255129Subproblem 2
x + 3.5 = -1.224744871 Simplifying x + 3.5 = -1.224744871 Reorder the terms: 3.5 + x = -1.224744871 Solving 3.5 + x = -1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -1.224744871 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -1.224744871 + -3.5 x = -1.224744871 + -3.5 Combine like terms: -1.224744871 + -3.5 = -4.724744871 x = -4.724744871 Simplifying x = -4.724744871Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.275255129, -4.724744871}
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