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Simplifying 4000 = 3.51x2 + 24.4x + 780 Reorder the terms: 4000 = 780 + 24.4x + 3.51x2 Solving 4000 = 780 + 24.4x + 3.51x2 Solving for variable 'x'. Combine like terms: 4000 + -780 = 3220 3220 + -24.4x + -3.51x2 = 780 + 24.4x + 3.51x2 + -780 + -24.4x + -3.51x2 Reorder the terms: 3220 + -24.4x + -3.51x2 = 780 + -780 + 24.4x + -24.4x + 3.51x2 + -3.51x2 Combine like terms: 780 + -780 = 0 3220 + -24.4x + -3.51x2 = 0 + 24.4x + -24.4x + 3.51x2 + -3.51x2 3220 + -24.4x + -3.51x2 = 24.4x + -24.4x + 3.51x2 + -3.51x2 Combine like terms: 24.4x + -24.4x = 0.0 3220 + -24.4x + -3.51x2 = 0.0 + 3.51x2 + -3.51x2 3220 + -24.4x + -3.51x2 = 3.51x2 + -3.51x2 Combine like terms: 3.51x2 + -3.51x2 = 0.00 3220 + -24.4x + -3.51x2 = 0.00 Begin completing the square. Divide all terms by -3.51 the coefficient of the squared term: Divide each side by '-3.51'. -917.3789174 + 6.951566952x + x2 = 0 Move the constant term to the right: Add '917.3789174' to each side of the equation. -917.3789174 + 6.951566952x + 917.3789174 + x2 = 0 + 917.3789174 Reorder the terms: -917.3789174 + 917.3789174 + 6.951566952x + x2 = 0 + 917.3789174 Combine like terms: -917.3789174 + 917.3789174 = 0.0000000 0.0000000 + 6.951566952x + x2 = 0 + 917.3789174 6.951566952x + x2 = 0 + 917.3789174 Combine like terms: 0 + 917.3789174 = 917.3789174 6.951566952x + x2 = 917.3789174 The x term is 6.951566952x. Take half its coefficient (3.475783476). Square it (12.08107077) and add it to both sides. Add '12.08107077' to each side of the equation. 6.951566952x + 12.08107077 + x2 = 917.3789174 + 12.08107077 Reorder the terms: 12.08107077 + 6.951566952x + x2 = 917.3789174 + 12.08107077 Combine like terms: 917.3789174 + 12.08107077 = 929.45998817 12.08107077 + 6.951566952x + x2 = 929.45998817 Factor a perfect square on the left side: (x + 3.475783476)(x + 3.475783476) = 929.45998817 Calculate the square root of the right side: 30.487046236 Break this problem into two subproblems by setting (x + 3.475783476) equal to 30.487046236 and -30.487046236.Subproblem 1
x + 3.475783476 = 30.487046236 Simplifying x + 3.475783476 = 30.487046236 Reorder the terms: 3.475783476 + x = 30.487046236 Solving 3.475783476 + x = 30.487046236 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.475783476' to each side of the equation. 3.475783476 + -3.475783476 + x = 30.487046236 + -3.475783476 Combine like terms: 3.475783476 + -3.475783476 = 0.000000000 0.000000000 + x = 30.487046236 + -3.475783476 x = 30.487046236 + -3.475783476 Combine like terms: 30.487046236 + -3.475783476 = 27.01126276 x = 27.01126276 Simplifying x = 27.01126276Subproblem 2
x + 3.475783476 = -30.487046236 Simplifying x + 3.475783476 = -30.487046236 Reorder the terms: 3.475783476 + x = -30.487046236 Solving 3.475783476 + x = -30.487046236 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.475783476' to each side of the equation. 3.475783476 + -3.475783476 + x = -30.487046236 + -3.475783476 Combine like terms: 3.475783476 + -3.475783476 = 0.000000000 0.000000000 + x = -30.487046236 + -3.475783476 x = -30.487046236 + -3.475783476 Combine like terms: -30.487046236 + -3.475783476 = -33.962829712 x = -33.962829712 Simplifying x = -33.962829712Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.01126276, -33.962829712}
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