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Simplifying 30 = -0.1x2 + 23x + -400 Reorder the terms: 30 = -400 + 23x + -0.1x2 Solving 30 = -400 + 23x + -0.1x2 Solving for variable 'x'. Combine like terms: 30 + 400 = 430 430 + -23x + 0.1x2 = -400 + 23x + -0.1x2 + 400 + -23x + 0.1x2 Reorder the terms: 430 + -23x + 0.1x2 = -400 + 400 + 23x + -23x + -0.1x2 + 0.1x2 Combine like terms: -400 + 400 = 0 430 + -23x + 0.1x2 = 0 + 23x + -23x + -0.1x2 + 0.1x2 430 + -23x + 0.1x2 = 23x + -23x + -0.1x2 + 0.1x2 Combine like terms: 23x + -23x = 0 430 + -23x + 0.1x2 = 0 + -0.1x2 + 0.1x2 430 + -23x + 0.1x2 = -0.1x2 + 0.1x2 Combine like terms: -0.1x2 + 0.1x2 = 0.0 430 + -23x + 0.1x2 = 0.0 Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. 4300 + -230x + x2 = 0 Move the constant term to the right: Add '-4300' to each side of the equation. 4300 + -230x + -4300 + x2 = 0 + -4300 Reorder the terms: 4300 + -4300 + -230x + x2 = 0 + -4300 Combine like terms: 4300 + -4300 = 0 0 + -230x + x2 = 0 + -4300 -230x + x2 = 0 + -4300 Combine like terms: 0 + -4300 = -4300 -230x + x2 = -4300 The x term is -230x. Take half its coefficient (-115). Square it (13225) and add it to both sides. Add '13225' to each side of the equation. -230x + 13225 + x2 = -4300 + 13225 Reorder the terms: 13225 + -230x + x2 = -4300 + 13225 Combine like terms: -4300 + 13225 = 8925 13225 + -230x + x2 = 8925 Factor a perfect square on the left side: (x + -115)(x + -115) = 8925 Calculate the square root of the right side: 94.472218138 Break this problem into two subproblems by setting (x + -115) equal to 94.472218138 and -94.472218138.Subproblem 1
x + -115 = 94.472218138 Simplifying x + -115 = 94.472218138 Reorder the terms: -115 + x = 94.472218138 Solving -115 + x = 94.472218138 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '115' to each side of the equation. -115 + 115 + x = 94.472218138 + 115 Combine like terms: -115 + 115 = 0 0 + x = 94.472218138 + 115 x = 94.472218138 + 115 Combine like terms: 94.472218138 + 115 = 209.472218138 x = 209.472218138 Simplifying x = 209.472218138Subproblem 2
x + -115 = -94.472218138 Simplifying x + -115 = -94.472218138 Reorder the terms: -115 + x = -94.472218138 Solving -115 + x = -94.472218138 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '115' to each side of the equation. -115 + 115 + x = -94.472218138 + 115 Combine like terms: -115 + 115 = 0 0 + x = -94.472218138 + 115 x = -94.472218138 + 115 Combine like terms: -94.472218138 + 115 = 20.527781862 x = 20.527781862 Simplifying x = 20.527781862Solution
The solution to the problem is based on the solutions from the subproblems. x = {209.472218138, 20.527781862}
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