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Simplifying 5x2 + -96x + -2000 = 0 Reorder the terms: -2000 + -96x + 5x2 = 0 Solving -2000 + -96x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -400 + -19.2x + x2 = 0 Move the constant term to the right: Add '400' to each side of the equation. -400 + -19.2x + 400 + x2 = 0 + 400 Reorder the terms: -400 + 400 + -19.2x + x2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + -19.2x + x2 = 0 + 400 -19.2x + x2 = 0 + 400 Combine like terms: 0 + 400 = 400 -19.2x + x2 = 400 The x term is -19.2x. Take half its coefficient (-9.6). Square it (92.16) and add it to both sides. Add '92.16' to each side of the equation. -19.2x + 92.16 + x2 = 400 + 92.16 Reorder the terms: 92.16 + -19.2x + x2 = 400 + 92.16 Combine like terms: 400 + 92.16 = 492.16 92.16 + -19.2x + x2 = 492.16 Factor a perfect square on the left side: (x + -9.6)(x + -9.6) = 492.16 Calculate the square root of the right side: 22.184679398 Break this problem into two subproblems by setting (x + -9.6) equal to 22.184679398 and -22.184679398.Subproblem 1
x + -9.6 = 22.184679398 Simplifying x + -9.6 = 22.184679398 Reorder the terms: -9.6 + x = 22.184679398 Solving -9.6 + x = 22.184679398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.6' to each side of the equation. -9.6 + 9.6 + x = 22.184679398 + 9.6 Combine like terms: -9.6 + 9.6 = 0.0 0.0 + x = 22.184679398 + 9.6 x = 22.184679398 + 9.6 Combine like terms: 22.184679398 + 9.6 = 31.784679398 x = 31.784679398 Simplifying x = 31.784679398Subproblem 2
x + -9.6 = -22.184679398 Simplifying x + -9.6 = -22.184679398 Reorder the terms: -9.6 + x = -22.184679398 Solving -9.6 + x = -22.184679398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.6' to each side of the equation. -9.6 + 9.6 + x = -22.184679398 + 9.6 Combine like terms: -9.6 + 9.6 = 0.0 0.0 + x = -22.184679398 + 9.6 x = -22.184679398 + 9.6 Combine like terms: -22.184679398 + 9.6 = -12.584679398 x = -12.584679398 Simplifying x = -12.584679398Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.784679398, -12.584679398}
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