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Simplifying x2 + 0.83x + -0.3 = 0 Reorder the terms: -0.3 + 0.83x + x2 = 0 Solving -0.3 + 0.83x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + 0.83x + 0.3 + x2 = 0 + 0.3 Reorder the terms: -0.3 + 0.3 + 0.83x + x2 = 0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + 0.83x + x2 = 0 + 0.3 0.83x + x2 = 0 + 0.3 Combine like terms: 0 + 0.3 = 0.3 0.83x + x2 = 0.3 The x term is 0.83x. Take half its coefficient (0.415). Square it (0.172225) and add it to both sides. Add '0.172225' to each side of the equation. 0.83x + 0.172225 + x2 = 0.3 + 0.172225 Reorder the terms: 0.172225 + 0.83x + x2 = 0.3 + 0.172225 Combine like terms: 0.3 + 0.172225 = 0.472225 0.172225 + 0.83x + x2 = 0.472225 Factor a perfect square on the left side: (x + 0.415)(x + 0.415) = 0.472225 Calculate the square root of the right side: 0.687186292 Break this problem into two subproblems by setting (x + 0.415) equal to 0.687186292 and -0.687186292.Subproblem 1
x + 0.415 = 0.687186292 Simplifying x + 0.415 = 0.687186292 Reorder the terms: 0.415 + x = 0.687186292 Solving 0.415 + x = 0.687186292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.415' to each side of the equation. 0.415 + -0.415 + x = 0.687186292 + -0.415 Combine like terms: 0.415 + -0.415 = 0.000 0.000 + x = 0.687186292 + -0.415 x = 0.687186292 + -0.415 Combine like terms: 0.687186292 + -0.415 = 0.272186292 x = 0.272186292 Simplifying x = 0.272186292Subproblem 2
x + 0.415 = -0.687186292 Simplifying x + 0.415 = -0.687186292 Reorder the terms: 0.415 + x = -0.687186292 Solving 0.415 + x = -0.687186292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.415' to each side of the equation. 0.415 + -0.415 + x = -0.687186292 + -0.415 Combine like terms: 0.415 + -0.415 = 0.000 0.000 + x = -0.687186292 + -0.415 x = -0.687186292 + -0.415 Combine like terms: -0.687186292 + -0.415 = -1.102186292 x = -1.102186292 Simplifying x = -1.102186292Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.272186292, -1.102186292}
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