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Simplifying 0.8x2 + -0.12x + -0.13 = 0 Reorder the terms: -0.13 + -0.12x + 0.8x2 = 0 Solving -0.13 + -0.12x + 0.8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.8 the coefficient of the squared term: Divide each side by '0.8'. -0.1625 + -0.15x + x2 = 0 Move the constant term to the right: Add '0.1625' to each side of the equation. -0.1625 + -0.15x + 0.1625 + x2 = 0 + 0.1625 Reorder the terms: -0.1625 + 0.1625 + -0.15x + x2 = 0 + 0.1625 Combine like terms: -0.1625 + 0.1625 = 0.0000 0.0000 + -0.15x + x2 = 0 + 0.1625 -0.15x + x2 = 0 + 0.1625 Combine like terms: 0 + 0.1625 = 0.1625 -0.15x + x2 = 0.1625 The x term is -0.15x. Take half its coefficient (-0.075). Square it (0.005625) and add it to both sides. Add '0.005625' to each side of the equation. -0.15x + 0.005625 + x2 = 0.1625 + 0.005625 Reorder the terms: 0.005625 + -0.15x + x2 = 0.1625 + 0.005625 Combine like terms: 0.1625 + 0.005625 = 0.168125 0.005625 + -0.15x + x2 = 0.168125 Factor a perfect square on the left side: (x + -0.075)(x + -0.075) = 0.168125 Calculate the square root of the right side: 0.410030487 Break this problem into two subproblems by setting (x + -0.075) equal to 0.410030487 and -0.410030487.Subproblem 1
x + -0.075 = 0.410030487 Simplifying x + -0.075 = 0.410030487 Reorder the terms: -0.075 + x = 0.410030487 Solving -0.075 + x = 0.410030487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.075' to each side of the equation. -0.075 + 0.075 + x = 0.410030487 + 0.075 Combine like terms: -0.075 + 0.075 = 0.000 0.000 + x = 0.410030487 + 0.075 x = 0.410030487 + 0.075 Combine like terms: 0.410030487 + 0.075 = 0.485030487 x = 0.485030487 Simplifying x = 0.485030487Subproblem 2
x + -0.075 = -0.410030487 Simplifying x + -0.075 = -0.410030487 Reorder the terms: -0.075 + x = -0.410030487 Solving -0.075 + x = -0.410030487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.075' to each side of the equation. -0.075 + 0.075 + x = -0.410030487 + 0.075 Combine like terms: -0.075 + 0.075 = 0.000 0.000 + x = -0.410030487 + 0.075 x = -0.410030487 + 0.075 Combine like terms: -0.410030487 + 0.075 = -0.335030487 x = -0.335030487 Simplifying x = -0.335030487Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.485030487, -0.335030487}
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