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Simplifying (2x2) + -8x + -143 = 0 Reorder the terms: -143 + -8x + (2x2) = 0 Solving -143 + -8x + (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'. -71.5 + -4x + x2 = 0 Move the constant term to the right: Add '71.5' to each side of the equation. -71.5 + -4x + 71.5 + x2 = 0 + 71.5 Reorder the terms: -71.5 + 71.5 + -4x + x2 = 0 + 71.5 Combine like terms: -71.5 + 71.5 = 0.0 0.0 + -4x + x2 = 0 + 71.5 -4x + x2 = 0 + 71.5 Combine like terms: 0 + 71.5 = 71.5 -4x + x2 = 71.5 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 = 71.5 + 4 Reorder the terms: 4 + -4x + x2 = 71.5 + 4 Combine like terms: 71.5 + 4 = 75.5 4 + -4x + x2 = 75.5 Factor a perfect square on the left side: ((x) + -2)((x) + -2) = 75.5 Calculate the square root of the right side: 8.689073598 Break this problem into two subproblems by setting ((x) + -2) equal to 8.689073598 and -8.689073598.Subproblem 1
(x) + -2 = 8.689073598 Simplifying (x) + -2 = 8.689073598 x + -2 = 8.689073598 Reorder the terms: -2 + x = 8.689073598 Solving -2 + x = 8.689073598 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 = 8.689073598 + 2 Combine like terms: -2 + 2 = 0 0 + x = 8.689073598 + 2 x = 8.689073598 + 2 Combine like terms: 8.689073598 + 2 = 10.689073598 x = 10.689073598 Simplifying x = 10.689073598Subproblem 2
(x) + -2 = -8.689073598 Simplifying (x) + -2 = -8.689073598 x + -2 = -8.689073598 Reorder the terms: -2 + x = -8.689073598 Solving -2 + x = -8.689073598 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 = -8.689073598 + 2 Combine like terms: -2 + 2 = 0 0 + x = -8.689073598 + 2 x = -8.689073598 + 2 Combine like terms: -8.689073598 + 2 = -6.689073598 x = -6.689073598 Simplifying x = -6.689073598Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.689073598, -6.689073598}
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