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Simplifying 0.5x2 + 140x + -9600 = 0 Reorder the terms: -9600 + 140x + 0.5x2 = 0 Solving -9600 + 140x + 0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -19200 + 280x + x2 = 0 Move the constant term to the right: Add '19200' to each side of the equation. -19200 + 280x + 19200 + x2 = 0 + 19200 Reorder the terms: -19200 + 19200 + 280x + x2 = 0 + 19200 Combine like terms: -19200 + 19200 = 0 0 + 280x + x2 = 0 + 19200 280x + x2 = 0 + 19200 Combine like terms: 0 + 19200 = 19200 280x + x2 = 19200 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 = 19200 + 19600 Reorder the terms: 19600 + 280x + x2 = 19200 + 19600 Combine like terms: 19200 + 19600 = 38800 19600 + 280x + x2 = 38800 Factor a perfect square on the left side: (x + 140)(x + 140) = 38800 Calculate the square root of the right side: 196.977156036 Break this problem into two subproblems by setting (x + 140) equal to 196.977156036 and -196.977156036.Subproblem 1
x + 140 = 196.977156036 Simplifying x + 140 = 196.977156036 Reorder the terms: 140 + x = 196.977156036 Solving 140 + x = 196.977156036 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 = 196.977156036 + -140 Combine like terms: 140 + -140 = 0 0 + x = 196.977156036 + -140 x = 196.977156036 + -140 Combine like terms: 196.977156036 + -140 = 56.977156036 x = 56.977156036 Simplifying x = 56.977156036Subproblem 2
x + 140 = -196.977156036 Simplifying x + 140 = -196.977156036 Reorder the terms: 140 + x = -196.977156036 Solving 140 + x = -196.977156036 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 = -196.977156036 + -140 Combine like terms: 140 + -140 = 0 0 + x = -196.977156036 + -140 x = -196.977156036 + -140 Combine like terms: -196.977156036 + -140 = -336.977156036 x = -336.977156036 Simplifying x = -336.977156036Solution
The solution to the problem is based on the solutions from the subproblems. x = {56.977156036, -336.977156036}
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