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Simplifying x2 + 1.667x + -0.833 = 0 Reorder the terms: -0.833 + 1.667x + x2 = 0 Solving -0.833 + 1.667x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.833' to each side of the equation. -0.833 + 1.667x + 0.833 + x2 = 0 + 0.833 Reorder the terms: -0.833 + 0.833 + 1.667x + x2 = 0 + 0.833 Combine like terms: -0.833 + 0.833 = 0.000 0.000 + 1.667x + x2 = 0 + 0.833 1.667x + x2 = 0 + 0.833 Combine like terms: 0 + 0.833 = 0.833 1.667x + x2 = 0.833 The x term is 1.667x. Take half its coefficient (0.8335). Square it (0.69472225) and add it to both sides. Add '0.69472225' to each side of the equation. 1.667x + 0.69472225 + x2 = 0.833 + 0.69472225 Reorder the terms: 0.69472225 + 1.667x + x2 = 0.833 + 0.69472225 Combine like terms: 0.833 + 0.69472225 = 1.52772225 0.69472225 + 1.667x + x2 = 1.52772225 Factor a perfect square on the left side: (x + 0.8335)(x + 0.8335) = 1.52772225 Calculate the square root of the right side: 1.236010619 Break this problem into two subproblems by setting (x + 0.8335) equal to 1.236010619 and -1.236010619.Subproblem 1
x + 0.8335 = 1.236010619 Simplifying x + 0.8335 = 1.236010619 Reorder the terms: 0.8335 + x = 1.236010619 Solving 0.8335 + x = 1.236010619 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8335' to each side of the equation. 0.8335 + -0.8335 + x = 1.236010619 + -0.8335 Combine like terms: 0.8335 + -0.8335 = 0.0000 0.0000 + x = 1.236010619 + -0.8335 x = 1.236010619 + -0.8335 Combine like terms: 1.236010619 + -0.8335 = 0.402510619 x = 0.402510619 Simplifying x = 0.402510619Subproblem 2
x + 0.8335 = -1.236010619 Simplifying x + 0.8335 = -1.236010619 Reorder the terms: 0.8335 + x = -1.236010619 Solving 0.8335 + x = -1.236010619 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8335' to each side of the equation. 0.8335 + -0.8335 + x = -1.236010619 + -0.8335 Combine like terms: 0.8335 + -0.8335 = 0.0000 0.0000 + x = -1.236010619 + -0.8335 x = -1.236010619 + -0.8335 Combine like terms: -1.236010619 + -0.8335 = -2.069510619 x = -2.069510619 Simplifying x = -2.069510619Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.402510619, -2.069510619}
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