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Simplifying 40x + -1x2 + -192 = 0 Reorder the terms: -192 + 40x + -1x2 = 0 Solving -192 + 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'. 192 + -40x + x2 = 0 Move the constant term to the right: Add '-192' to each side of the equation. 192 + -40x + -192 + x2 = 0 + -192 Reorder the terms: 192 + -192 + -40x + x2 = 0 + -192 Combine like terms: 192 + -192 = 0 0 + -40x + x2 = 0 + -192 -40x + x2 = 0 + -192 Combine like terms: 0 + -192 = -192 -40x + x2 = -192 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 = -192 + 400 Reorder the terms: 400 + -40x + x2 = -192 + 400 Combine like terms: -192 + 400 = 208 400 + -40x + x2 = 208 Factor a perfect square on the left side: (x + -20)(x + -20) = 208 Calculate the square root of the right side: 14.422205102 Break this problem into two subproblems by setting (x + -20) equal to 14.422205102 and -14.422205102.Subproblem 1
x + -20 = 14.422205102 Simplifying x + -20 = 14.422205102 Reorder the terms: -20 + x = 14.422205102 Solving -20 + x = 14.422205102 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 = 14.422205102 + 20 Combine like terms: -20 + 20 = 0 0 + x = 14.422205102 + 20 x = 14.422205102 + 20 Combine like terms: 14.422205102 + 20 = 34.422205102 x = 34.422205102 Simplifying x = 34.422205102Subproblem 2
x + -20 = -14.422205102 Simplifying x + -20 = -14.422205102 Reorder the terms: -20 + x = -14.422205102 Solving -20 + x = -14.422205102 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 = -14.422205102 + 20 Combine like terms: -20 + 20 = 0 0 + x = -14.422205102 + 20 x = -14.422205102 + 20 Combine like terms: -14.422205102 + 20 = 5.577794898 x = 5.577794898 Simplifying x = 5.577794898Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.422205102, 5.577794898}
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