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Simplifying 0.93x2 + 22x + 130 = 164 Reorder the terms: 130 + 22x + 0.93x2 = 164 Solving 130 + 22x + 0.93x2 = 164 Solving for variable 'x'. Reorder the terms: 130 + -164 + 22x + 0.93x2 = 164 + -164 Combine like terms: 130 + -164 = -34 -34 + 22x + 0.93x2 = 164 + -164 Combine like terms: 164 + -164 = 0 -34 + 22x + 0.93x2 = 0 Begin completing the square. Divide all terms by 0.93 the coefficient of the squared term: Divide each side by '0.93'. -36.55913978 + 23.65591398x + x2 = 0 Move the constant term to the right: Add '36.55913978' to each side of the equation. -36.55913978 + 23.65591398x + 36.55913978 + x2 = 0 + 36.55913978 Reorder the terms: -36.55913978 + 36.55913978 + 23.65591398x + x2 = 0 + 36.55913978 Combine like terms: -36.55913978 + 36.55913978 = 0.00000000 0.00000000 + 23.65591398x + x2 = 0 + 36.55913978 23.65591398x + x2 = 0 + 36.55913978 Combine like terms: 0 + 36.55913978 = 36.55913978 23.65591398x + x2 = 36.55913978 The x term is 23.65591398x. Take half its coefficient (11.82795699). Square it (139.9005666) and add it to both sides. Add '139.9005666' to each side of the equation. 23.65591398x + 139.9005666 + x2 = 36.55913978 + 139.9005666 Reorder the terms: 139.9005666 + 23.65591398x + x2 = 36.55913978 + 139.9005666 Combine like terms: 36.55913978 + 139.9005666 = 176.45970638 139.9005666 + 23.65591398x + x2 = 176.45970638 Factor a perfect square on the left side: (x + 11.82795699)(x + 11.82795699) = 176.45970638 Calculate the square root of the right side: 13.283813699 Break this problem into two subproblems by setting (x + 11.82795699) equal to 13.283813699 and -13.283813699.Subproblem 1
x + 11.82795699 = 13.283813699 Simplifying x + 11.82795699 = 13.283813699 Reorder the terms: 11.82795699 + x = 13.283813699 Solving 11.82795699 + x = 13.283813699 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.82795699' to each side of the equation. 11.82795699 + -11.82795699 + x = 13.283813699 + -11.82795699 Combine like terms: 11.82795699 + -11.82795699 = 0.00000000 0.00000000 + x = 13.283813699 + -11.82795699 x = 13.283813699 + -11.82795699 Combine like terms: 13.283813699 + -11.82795699 = 1.455856709 x = 1.455856709 Simplifying x = 1.455856709Subproblem 2
x + 11.82795699 = -13.283813699 Simplifying x + 11.82795699 = -13.283813699 Reorder the terms: 11.82795699 + x = -13.283813699 Solving 11.82795699 + x = -13.283813699 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.82795699' to each side of the equation. 11.82795699 + -11.82795699 + x = -13.283813699 + -11.82795699 Combine like terms: 11.82795699 + -11.82795699 = 0.00000000 0.00000000 + x = -13.283813699 + -11.82795699 x = -13.283813699 + -11.82795699 Combine like terms: -13.283813699 + -11.82795699 = -25.111770689 x = -25.111770689 Simplifying x = -25.111770689Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.455856709, -25.111770689}
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