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Simplifying 115x + -0.5x2 = 400 Solving 115x + -0.5x2 = 400 Solving for variable 'x'. Reorder the terms: -400 + 115x + -0.5x2 = 400 + -400 Combine like terms: 400 + -400 = 0 -400 + 115x + -0.5x2 = 0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. 800 + -230x + x2 = 0 Move the constant term to the right: Add '-800' to each side of the equation. 800 + -230x + -800 + x2 = 0 + -800 Reorder the terms: 800 + -800 + -230x + x2 = 0 + -800 Combine like terms: 800 + -800 = 0 0 + -230x + x2 = 0 + -800 -230x + x2 = 0 + -800 Combine like terms: 0 + -800 = -800 -230x + x2 = -800 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 = -800 + 13225 Reorder the terms: 13225 + -230x + x2 = -800 + 13225 Combine like terms: -800 + 13225 = 12425 13225 + -230x + x2 = 12425 Factor a perfect square on the left side: (x + -115)(x + -115) = 12425 Calculate the square root of the right side: 111.467484048 Break this problem into two subproblems by setting (x + -115) equal to 111.467484048 and -111.467484048.Subproblem 1
x + -115 = 111.467484048 Simplifying x + -115 = 111.467484048 Reorder the terms: -115 + x = 111.467484048 Solving -115 + x = 111.467484048 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 = 111.467484048 + 115 Combine like terms: -115 + 115 = 0 0 + x = 111.467484048 + 115 x = 111.467484048 + 115 Combine like terms: 111.467484048 + 115 = 226.467484048 x = 226.467484048 Simplifying x = 226.467484048Subproblem 2
x + -115 = -111.467484048 Simplifying x + -115 = -111.467484048 Reorder the terms: -115 + x = -111.467484048 Solving -115 + x = -111.467484048 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 = -111.467484048 + 115 Combine like terms: -115 + 115 = 0 0 + x = -111.467484048 + 115 x = -111.467484048 + 115 Combine like terms: -111.467484048 + 115 = 3.532515952 x = 3.532515952 Simplifying x = 3.532515952Solution
The solution to the problem is based on the solutions from the subproblems. x = {226.467484048, 3.532515952}
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