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Simplifying 1.4286x2 + -10.8286x + 19.4 = 100 Reorder the terms: 19.4 + -10.8286x + 1.4286x2 = 100 Solving 19.4 + -10.8286x + 1.4286x2 = 100 Solving for variable 'x'. Reorder the terms: 19.4 + -100 + -10.8286x + 1.4286x2 = 100 + -100 Combine like terms: 19.4 + -100 = -80.6 -80.6 + -10.8286x + 1.4286x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -80.6 + -10.8286x + 1.4286x2 = 0 Begin completing the square. Divide all terms by 1.4286 the coefficient of the squared term: Divide each side by '1.4286'. -56.41887162 + -7.579868403x + x2 = 0 Move the constant term to the right: Add '56.41887162' to each side of the equation. -56.41887162 + -7.579868403x + 56.41887162 + x2 = 0 + 56.41887162 Reorder the terms: -56.41887162 + 56.41887162 + -7.579868403x + x2 = 0 + 56.41887162 Combine like terms: -56.41887162 + 56.41887162 = 0.00000000 0.00000000 + -7.579868403x + x2 = 0 + 56.41887162 -7.579868403x + x2 = 0 + 56.41887162 Combine like terms: 0 + 56.41887162 = 56.41887162 -7.579868403x + x2 = 56.41887162 The x term is -7.579868403x. Take half its coefficient (-3.789934202). Square it (14.36360126) and add it to both sides. Add '14.36360126' to each side of the equation. -7.579868403x + 14.36360126 + x2 = 56.41887162 + 14.36360126 Reorder the terms: 14.36360126 + -7.579868403x + x2 = 56.41887162 + 14.36360126 Combine like terms: 56.41887162 + 14.36360126 = 70.78247288 14.36360126 + -7.579868403x + x2 = 70.78247288 Factor a perfect square on the left side: (x + -3.789934202)(x + -3.789934202) = 70.78247288 Calculate the square root of the right side: 8.413232012 Break this problem into two subproblems by setting (x + -3.789934202) equal to 8.413232012 and -8.413232012.Subproblem 1
x + -3.789934202 = 8.413232012 Simplifying x + -3.789934202 = 8.413232012 Reorder the terms: -3.789934202 + x = 8.413232012 Solving -3.789934202 + x = 8.413232012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.789934202' to each side of the equation. -3.789934202 + 3.789934202 + x = 8.413232012 + 3.789934202 Combine like terms: -3.789934202 + 3.789934202 = 0.000000000 0.000000000 + x = 8.413232012 + 3.789934202 x = 8.413232012 + 3.789934202 Combine like terms: 8.413232012 + 3.789934202 = 12.203166214 x = 12.203166214 Simplifying x = 12.203166214Subproblem 2
x + -3.789934202 = -8.413232012 Simplifying x + -3.789934202 = -8.413232012 Reorder the terms: -3.789934202 + x = -8.413232012 Solving -3.789934202 + x = -8.413232012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.789934202' to each side of the equation. -3.789934202 + 3.789934202 + x = -8.413232012 + 3.789934202 Combine like terms: -3.789934202 + 3.789934202 = 0.000000000 0.000000000 + x = -8.413232012 + 3.789934202 x = -8.413232012 + 3.789934202 Combine like terms: -8.413232012 + 3.789934202 = -4.62329781 x = -4.62329781 Simplifying x = -4.62329781Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.203166214, -4.62329781}
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