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Simplifying 40x + -1x2 + -96 = 0 Reorder the terms: -96 + 40x + -1x2 = 0 Solving -96 + 40x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 96 + -40x + x2 = 0 Move the constant term to the right: Add '-96' to each side of the equation. 96 + -40x + -96 + x2 = 0 + -96 Reorder the terms: 96 + -96 + -40x + x2 = 0 + -96 Combine like terms: 96 + -96 = 0 0 + -40x + x2 = 0 + -96 -40x + x2 = 0 + -96 Combine like terms: 0 + -96 = -96 -40x + x2 = -96 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = -96 + 400 Reorder the terms: 400 + -40x + x2 = -96 + 400 Combine like terms: -96 + 400 = 304 400 + -40x + x2 = 304 Factor a perfect square on the left side: (x + -20)(x + -20) = 304 Calculate the square root of the right side: 17.435595774 Break this problem into two subproblems by setting (x + -20) equal to 17.435595774 and -17.435595774.Subproblem 1
x + -20 = 17.435595774 Simplifying x + -20 = 17.435595774 Reorder the terms: -20 + x = 17.435595774 Solving -20 + x = 17.435595774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 17.435595774 + 20 Combine like terms: -20 + 20 = 0 0 + x = 17.435595774 + 20 x = 17.435595774 + 20 Combine like terms: 17.435595774 + 20 = 37.435595774 x = 37.435595774 Simplifying x = 37.435595774Subproblem 2
x + -20 = -17.435595774 Simplifying x + -20 = -17.435595774 Reorder the terms: -20 + x = -17.435595774 Solving -20 + x = -17.435595774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -17.435595774 + 20 Combine like terms: -20 + 20 = 0 0 + x = -17.435595774 + 20 x = -17.435595774 + 20 Combine like terms: -17.435595774 + 20 = 2.564404226 x = 2.564404226 Simplifying x = 2.564404226Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.435595774, 2.564404226}
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