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Simplifying 19175 + -112x = 0.4x2 Solving 19175 + -112x = 0.4x2 Solving for variable 'x'. Combine like terms: 0.4x2 + -0.4x2 = 0.0 19175 + -112x + -0.4x2 = 0.0 Begin completing the square. Divide all terms by -0.4 the coefficient of the squared term: Divide each side by '-0.4'. -47937.5 + 280x + x2 = 0 Move the constant term to the right: Add '47937.5' to each side of the equation. -47937.5 + 280x + 47937.5 + x2 = 0 + 47937.5 Reorder the terms: -47937.5 + 47937.5 + 280x + x2 = 0 + 47937.5 Combine like terms: -47937.5 + 47937.5 = 0.0 0.0 + 280x + x2 = 0 + 47937.5 280x + x2 = 0 + 47937.5 Combine like terms: 0 + 47937.5 = 47937.5 280x + x2 = 47937.5 The x term is 280x. Take half its coefficient (140). Square it (19600) and add it to both sides. Add '19600' to each side of the equation. 280x + 19600 + x2 = 47937.5 + 19600 Reorder the terms: 19600 + 280x + x2 = 47937.5 + 19600 Combine like terms: 47937.5 + 19600 = 67537.5 19600 + 280x + x2 = 67537.5 Factor a perfect square on the left side: (x + 140)(x + 140) = 67537.5 Calculate the square root of the right side: 259.879779898 Break this problem into two subproblems by setting (x + 140) equal to 259.879779898 and -259.879779898.Subproblem 1
x + 140 = 259.879779898 Simplifying x + 140 = 259.879779898 Reorder the terms: 140 + x = 259.879779898 Solving 140 + x = 259.879779898 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-140' to each side of the equation. 140 + -140 + x = 259.879779898 + -140 Combine like terms: 140 + -140 = 0 0 + x = 259.879779898 + -140 x = 259.879779898 + -140 Combine like terms: 259.879779898 + -140 = 119.879779898 x = 119.879779898 Simplifying x = 119.879779898Subproblem 2
x + 140 = -259.879779898 Simplifying x + 140 = -259.879779898 Reorder the terms: 140 + x = -259.879779898 Solving 140 + x = -259.879779898 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-140' to each side of the equation. 140 + -140 + x = -259.879779898 + -140 Combine like terms: 140 + -140 = 0 0 + x = -259.879779898 + -140 x = -259.879779898 + -140 Combine like terms: -259.879779898 + -140 = -399.879779898 x = -399.879779898 Simplifying x = -399.879779898Solution
The solution to the problem is based on the solutions from the subproblems. x = {119.879779898, -399.879779898}
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