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Simplifying 0 = -4.9X2 + 16.6X + 58.8 Reorder the terms: 0 = 58.8 + 16.6X + -4.9X2 Solving 0 = 58.8 + 16.6X + -4.9X2 Solving for variable 'X'. Combine like terms: 0 + -58.8 = -58.8 -58.8 + -16.6X + 4.9X2 = 58.8 + 16.6X + -4.9X2 + -58.8 + -16.6X + 4.9X2 Reorder the terms: -58.8 + -16.6X + 4.9X2 = 58.8 + -58.8 + 16.6X + -16.6X + -4.9X2 + 4.9X2 Combine like terms: 58.8 + -58.8 = 0.0 -58.8 + -16.6X + 4.9X2 = 0.0 + 16.6X + -16.6X + -4.9X2 + 4.9X2 -58.8 + -16.6X + 4.9X2 = 16.6X + -16.6X + -4.9X2 + 4.9X2 Combine like terms: 16.6X + -16.6X = 0.0 -58.8 + -16.6X + 4.9X2 = 0.0 + -4.9X2 + 4.9X2 -58.8 + -16.6X + 4.9X2 = -4.9X2 + 4.9X2 Combine like terms: -4.9X2 + 4.9X2 = 0.0 -58.8 + -16.6X + 4.9X2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -12 + -3.387755102X + X2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -3.387755102X + 12 + X2 = 0 + 12 Reorder the terms: -12 + 12 + -3.387755102X + X2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -3.387755102X + X2 = 0 + 12 -3.387755102X + X2 = 0 + 12 Combine like terms: 0 + 12 = 12 -3.387755102X + X2 = 12 The X term is -3.387755102X. Take half its coefficient (-1.693877551). Square it (2.869221158) and add it to both sides. Add '2.869221158' to each side of the equation. -3.387755102X + 2.869221158 + X2 = 12 + 2.869221158 Reorder the terms: 2.869221158 + -3.387755102X + X2 = 12 + 2.869221158 Combine like terms: 12 + 2.869221158 = 14.869221158 2.869221158 + -3.387755102X + X2 = 14.869221158 Factor a perfect square on the left side: (X + -1.693877551)(X + -1.693877551) = 14.869221158 Calculate the square root of the right side: 3.856062909 Break this problem into two subproblems by setting (X + -1.693877551) equal to 3.856062909 and -3.856062909.Subproblem 1
X + -1.693877551 = 3.856062909 Simplifying X + -1.693877551 = 3.856062909 Reorder the terms: -1.693877551 + X = 3.856062909 Solving -1.693877551 + X = 3.856062909 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.693877551' to each side of the equation. -1.693877551 + 1.693877551 + X = 3.856062909 + 1.693877551 Combine like terms: -1.693877551 + 1.693877551 = 0.000000000 0.000000000 + X = 3.856062909 + 1.693877551 X = 3.856062909 + 1.693877551 Combine like terms: 3.856062909 + 1.693877551 = 5.54994046 X = 5.54994046 Simplifying X = 5.54994046Subproblem 2
X + -1.693877551 = -3.856062909 Simplifying X + -1.693877551 = -3.856062909 Reorder the terms: -1.693877551 + X = -3.856062909 Solving -1.693877551 + X = -3.856062909 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.693877551' to each side of the equation. -1.693877551 + 1.693877551 + X = -3.856062909 + 1.693877551 Combine like terms: -1.693877551 + 1.693877551 = 0.000000000 0.000000000 + X = -3.856062909 + 1.693877551 X = -3.856062909 + 1.693877551 Combine like terms: -3.856062909 + 1.693877551 = -2.162185358 X = -2.162185358 Simplifying X = -2.162185358Solution
The solution to the problem is based on the solutions from the subproblems. X = {5.54994046, -2.162185358}
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