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Simplifying (-16x2) + 45x + 2.5 = 0 Reorder the terms: 2.5 + 45x + (-16x2) = 0 Solving 2.5 + 45x + (-16x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.15625 + -2.8125x + x2 = 0 Move the constant term to the right: Add '0.15625' to each side of the equation. -0.15625 + -2.8125x + 0.15625 + x2 = 0 + 0.15625 Reorder the terms: -0.15625 + 0.15625 + -2.8125x + x2 = 0 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + -2.8125x + x2 = 0 + 0.15625 -2.8125x + x2 = 0 + 0.15625 Combine like terms: 0 + 0.15625 = 0.15625 -2.8125x + x2 = 0.15625 The x term is -2.8125x. Take half its coefficient (-1.40625). Square it (1.977539063) and add it to both sides. Add '1.977539063' to each side of the equation. -2.8125x + 1.977539063 + x2 = 0.15625 + 1.977539063 Reorder the terms: 1.977539063 + -2.8125x + x2 = 0.15625 + 1.977539063 Combine like terms: 0.15625 + 1.977539063 = 2.133789063 1.977539063 + -2.8125x + x2 = 2.133789063 Factor a perfect square on the left side: ((x) + -1.40625)((x) + -1.40625) = 2.133789063 Calculate the square root of the right side: 1.460749487 Break this problem into two subproblems by setting ((x) + -1.40625) equal to 1.460749487 and -1.460749487.Subproblem 1
(x) + -1.40625 = 1.460749487 Simplifying (x) + -1.40625 = 1.460749487 x + -1.40625 = 1.460749487 Reorder the terms: -1.40625 + x = 1.460749487 Solving -1.40625 + x = 1.460749487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.40625' to each side of the equation. -1.40625 + 1.40625 + x = 1.460749487 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + x = 1.460749487 + 1.40625 x = 1.460749487 + 1.40625 Combine like terms: 1.460749487 + 1.40625 = 2.866999487 x = 2.866999487 Simplifying x = 2.866999487Subproblem 2
(x) + -1.40625 = -1.460749487 Simplifying (x) + -1.40625 = -1.460749487 x + -1.40625 = -1.460749487 Reorder the terms: -1.40625 + x = -1.460749487 Solving -1.40625 + x = -1.460749487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.40625' to each side of the equation. -1.40625 + 1.40625 + x = -1.460749487 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + x = -1.460749487 + 1.40625 x = -1.460749487 + 1.40625 Combine like terms: -1.460749487 + 1.40625 = -0.054499487 x = -0.054499487 Simplifying x = -0.054499487Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.866999487, -0.054499487}
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