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Simplifying 0.39x2 + -140x + 10000 = 0 Reorder the terms: 10000 + -140x + 0.39x2 = 0 Solving 10000 + -140x + 0.39x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.39 the coefficient of the squared term: Divide each side by '0.39'. 25641.02564 + -358.974359x + x2 = 0 Move the constant term to the right: Add '-25641.02564' to each side of the equation. 25641.02564 + -358.974359x + -25641.02564 + x2 = 0 + -25641.02564 Reorder the terms: 25641.02564 + -25641.02564 + -358.974359x + x2 = 0 + -25641.02564 Combine like terms: 25641.02564 + -25641.02564 = 0.00000 0.00000 + -358.974359x + x2 = 0 + -25641.02564 -358.974359x + x2 = 0 + -25641.02564 Combine like terms: 0 + -25641.02564 = -25641.02564 -358.974359x + x2 = -25641.02564 The x term is -358.974359x. Take half its coefficient (-179.4871795). Square it (32215.64760) and add it to both sides. Add '32215.64760' to each side of the equation. -358.974359x + 32215.64760 + x2 = -25641.02564 + 32215.64760 Reorder the terms: 32215.64760 + -358.974359x + x2 = -25641.02564 + 32215.64760 Combine like terms: -25641.02564 + 32215.64760 = 6574.62196 32215.64760 + -358.974359x + x2 = 6574.62196 Factor a perfect square on the left side: (x + -179.4871795)(x + -179.4871795) = 6574.62196 Calculate the square root of the right side: 81.084042573 Break this problem into two subproblems by setting (x + -179.4871795) equal to 81.084042573 and -81.084042573.Subproblem 1
x + -179.4871795 = 81.084042573 Simplifying x + -179.4871795 = 81.084042573 Reorder the terms: -179.4871795 + x = 81.084042573 Solving -179.4871795 + x = 81.084042573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '179.4871795' to each side of the equation. -179.4871795 + 179.4871795 + x = 81.084042573 + 179.4871795 Combine like terms: -179.4871795 + 179.4871795 = 0.0000000 0.0000000 + x = 81.084042573 + 179.4871795 x = 81.084042573 + 179.4871795 Combine like terms: 81.084042573 + 179.4871795 = 260.571222073 x = 260.571222073 Simplifying x = 260.571222073Subproblem 2
x + -179.4871795 = -81.084042573 Simplifying x + -179.4871795 = -81.084042573 Reorder the terms: -179.4871795 + x = -81.084042573 Solving -179.4871795 + x = -81.084042573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '179.4871795' to each side of the equation. -179.4871795 + 179.4871795 + x = -81.084042573 + 179.4871795 Combine like terms: -179.4871795 + 179.4871795 = 0.0000000 0.0000000 + x = -81.084042573 + 179.4871795 x = -81.084042573 + 179.4871795 Combine like terms: -81.084042573 + 179.4871795 = 98.403136927 x = 98.403136927 Simplifying x = 98.403136927Solution
The solution to the problem is based on the solutions from the subproblems. x = {260.571222073, 98.403136927}
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