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Simplifying 2.5x2 + 9x + -3.14 = 0 Reorder the terms: -3.14 + 9x + 2.5x2 = 0 Solving -3.14 + 9x + 2.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.5 the coefficient of the squared term: Divide each side by '2.5'. -1.256 + 3.6x + x2 = 0 Move the constant term to the right: Add '1.256' to each side of the equation. -1.256 + 3.6x + 1.256 + x2 = 0 + 1.256 Reorder the terms: -1.256 + 1.256 + 3.6x + x2 = 0 + 1.256 Combine like terms: -1.256 + 1.256 = 0.000 0.000 + 3.6x + x2 = 0 + 1.256 3.6x + x2 = 0 + 1.256 Combine like terms: 0 + 1.256 = 1.256 3.6x + x2 = 1.256 The x term is 3.6x. Take half its coefficient (1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. 3.6x + 3.24 + x2 = 1.256 + 3.24 Reorder the terms: 3.24 + 3.6x + x2 = 1.256 + 3.24 Combine like terms: 1.256 + 3.24 = 4.496 3.24 + 3.6x + x2 = 4.496 Factor a perfect square on the left side: (x + 1.8)(x + 1.8) = 4.496 Calculate the square root of the right side: 2.120377325 Break this problem into two subproblems by setting (x + 1.8) equal to 2.120377325 and -2.120377325.Subproblem 1
x + 1.8 = 2.120377325 Simplifying x + 1.8 = 2.120377325 Reorder the terms: 1.8 + x = 2.120377325 Solving 1.8 + x = 2.120377325 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = 2.120377325 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = 2.120377325 + -1.8 x = 2.120377325 + -1.8 Combine like terms: 2.120377325 + -1.8 = 0.320377325 x = 0.320377325 Simplifying x = 0.320377325Subproblem 2
x + 1.8 = -2.120377325 Simplifying x + 1.8 = -2.120377325 Reorder the terms: 1.8 + x = -2.120377325 Solving 1.8 + x = -2.120377325 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = -2.120377325 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = -2.120377325 + -1.8 x = -2.120377325 + -1.8 Combine like terms: -2.120377325 + -1.8 = -3.920377325 x = -3.920377325 Simplifying x = -3.920377325Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.320377325, -3.920377325}
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