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Simplifying 0.0795x2 + -0.902x + 1.834 = 0 Reorder the terms: 1.834 + -0.902x + 0.0795x2 = 0 Solving 1.834 + -0.902x + 0.0795x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.0795 the coefficient of the squared term: Divide each side by '0.0795'. 23.06918239 + -11.34591195x + x2 = 0 Move the constant term to the right: Add '-23.06918239' to each side of the equation. 23.06918239 + -11.34591195x + -23.06918239 + x2 = 0 + -23.06918239 Reorder the terms: 23.06918239 + -23.06918239 + -11.34591195x + x2 = 0 + -23.06918239 Combine like terms: 23.06918239 + -23.06918239 = 0.00000000 0.00000000 + -11.34591195x + x2 = 0 + -23.06918239 -11.34591195x + x2 = 0 + -23.06918239 Combine like terms: 0 + -23.06918239 = -23.06918239 -11.34591195x + x2 = -23.06918239 The x term is -11.34591195x. Take half its coefficient (-5.672955975). Square it (32.18242949) and add it to both sides. Add '32.18242949' to each side of the equation. -11.34591195x + 32.18242949 + x2 = -23.06918239 + 32.18242949 Reorder the terms: 32.18242949 + -11.34591195x + x2 = -23.06918239 + 32.18242949 Combine like terms: -23.06918239 + 32.18242949 = 9.1132471 32.18242949 + -11.34591195x + x2 = 9.1132471 Factor a perfect square on the left side: (x + -5.672955975)(x + -5.672955975) = 9.1132471 Calculate the square root of the right side: 3.018815513 Break this problem into two subproblems by setting (x + -5.672955975) equal to 3.018815513 and -3.018815513.Subproblem 1
x + -5.672955975 = 3.018815513 Simplifying x + -5.672955975 = 3.018815513 Reorder the terms: -5.672955975 + x = 3.018815513 Solving -5.672955975 + x = 3.018815513 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.672955975' to each side of the equation. -5.672955975 + 5.672955975 + x = 3.018815513 + 5.672955975 Combine like terms: -5.672955975 + 5.672955975 = 0.000000000 0.000000000 + x = 3.018815513 + 5.672955975 x = 3.018815513 + 5.672955975 Combine like terms: 3.018815513 + 5.672955975 = 8.691771488 x = 8.691771488 Simplifying x = 8.691771488Subproblem 2
x + -5.672955975 = -3.018815513 Simplifying x + -5.672955975 = -3.018815513 Reorder the terms: -5.672955975 + x = -3.018815513 Solving -5.672955975 + x = -3.018815513 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.672955975' to each side of the equation. -5.672955975 + 5.672955975 + x = -3.018815513 + 5.672955975 Combine like terms: -5.672955975 + 5.672955975 = 0.000000000 0.000000000 + x = -3.018815513 + 5.672955975 x = -3.018815513 + 5.672955975 Combine like terms: -3.018815513 + 5.672955975 = 2.654140462 x = 2.654140462 Simplifying x = 2.654140462Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.691771488, 2.654140462}
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