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Simplifying 129 = 2x2 + -41x Reorder the terms: 129 = -41x + 2x2 Solving 129 = -41x + 2x2 Solving for variable 'x'. Reorder the terms: 129 + 41x + -2x2 = -41x + 41x + 2x2 + -2x2 Combine like terms: -41x + 41x = 0 129 + 41x + -2x2 = 0 + 2x2 + -2x2 129 + 41x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 129 + 41x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -64.5 + -20.5x + x2 = 0 Move the constant term to the right: Add '64.5' to each side of the equation. -64.5 + -20.5x + 64.5 + x2 = 0 + 64.5 Reorder the terms: -64.5 + 64.5 + -20.5x + x2 = 0 + 64.5 Combine like terms: -64.5 + 64.5 = 0.0 0.0 + -20.5x + x2 = 0 + 64.5 -20.5x + x2 = 0 + 64.5 Combine like terms: 0 + 64.5 = 64.5 -20.5x + x2 = 64.5 The x term is -20.5x. Take half its coefficient (-10.25). Square it (105.0625) and add it to both sides. Add '105.0625' to each side of the equation. -20.5x + 105.0625 + x2 = 64.5 + 105.0625 Reorder the terms: 105.0625 + -20.5x + x2 = 64.5 + 105.0625 Combine like terms: 64.5 + 105.0625 = 169.5625 105.0625 + -20.5x + x2 = 169.5625 Factor a perfect square on the left side: (x + -10.25)(x + -10.25) = 169.5625 Calculate the square root of the right side: 13.021616643 Break this problem into two subproblems by setting (x + -10.25) equal to 13.021616643 and -13.021616643.Subproblem 1
x + -10.25 = 13.021616643 Simplifying x + -10.25 = 13.021616643 Reorder the terms: -10.25 + x = 13.021616643 Solving -10.25 + x = 13.021616643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.25' to each side of the equation. -10.25 + 10.25 + x = 13.021616643 + 10.25 Combine like terms: -10.25 + 10.25 = 0.00 0.00 + x = 13.021616643 + 10.25 x = 13.021616643 + 10.25 Combine like terms: 13.021616643 + 10.25 = 23.271616643 x = 23.271616643 Simplifying x = 23.271616643Subproblem 2
x + -10.25 = -13.021616643 Simplifying x + -10.25 = -13.021616643 Reorder the terms: -10.25 + x = -13.021616643 Solving -10.25 + x = -13.021616643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.25' to each side of the equation. -10.25 + 10.25 + x = -13.021616643 + 10.25 Combine like terms: -10.25 + 10.25 = 0.00 0.00 + x = -13.021616643 + 10.25 x = -13.021616643 + 10.25 Combine like terms: -13.021616643 + 10.25 = -2.771616643 x = -2.771616643 Simplifying x = -2.771616643Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.271616643, -2.771616643}
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