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Simplifying 0 = 85 + 12x + -4.9x2 Solving 0 = 85 + 12x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -85 = -85 -85 + -12x + 4.9x2 = 85 + 12x + -4.9x2 + -85 + -12x + 4.9x2 Reorder the terms: -85 + -12x + 4.9x2 = 85 + -85 + 12x + -12x + -4.9x2 + 4.9x2 Combine like terms: 85 + -85 = 0 -85 + -12x + 4.9x2 = 0 + 12x + -12x + -4.9x2 + 4.9x2 -85 + -12x + 4.9x2 = 12x + -12x + -4.9x2 + 4.9x2 Combine like terms: 12x + -12x = 0 -85 + -12x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -85 + -12x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -85 + -12x + 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'. -17.34693878 + -2.448979592x + x2 = 0 Move the constant term to the right: Add '17.34693878' to each side of the equation. -17.34693878 + -2.448979592x + 17.34693878 + x2 = 0 + 17.34693878 Reorder the terms: -17.34693878 + 17.34693878 + -2.448979592x + x2 = 0 + 17.34693878 Combine like terms: -17.34693878 + 17.34693878 = 0.00000000 0.00000000 + -2.448979592x + x2 = 0 + 17.34693878 -2.448979592x + x2 = 0 + 17.34693878 Combine like terms: 0 + 17.34693878 = 17.34693878 -2.448979592x + x2 = 17.34693878 The x term is -2.448979592x. Take half its coefficient (-1.224489796). Square it (1.499375261) and add it to both sides. Add '1.499375261' to each side of the equation. -2.448979592x + 1.499375261 + x2 = 17.34693878 + 1.499375261 Reorder the terms: 1.499375261 + -2.448979592x + x2 = 17.34693878 + 1.499375261 Combine like terms: 17.34693878 + 1.499375261 = 18.846314041 1.499375261 + -2.448979592x + x2 = 18.846314041 Factor a perfect square on the left side: (x + -1.224489796)(x + -1.224489796) = 18.846314041 Calculate the square root of the right side: 4.341234161 Break this problem into two subproblems by setting (x + -1.224489796) equal to 4.341234161 and -4.341234161.Subproblem 1
x + -1.224489796 = 4.341234161 Simplifying x + -1.224489796 = 4.341234161 Reorder the terms: -1.224489796 + x = 4.341234161 Solving -1.224489796 + x = 4.341234161 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.224489796' to each side of the equation. -1.224489796 + 1.224489796 + x = 4.341234161 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + x = 4.341234161 + 1.224489796 x = 4.341234161 + 1.224489796 Combine like terms: 4.341234161 + 1.224489796 = 5.565723957 x = 5.565723957 Simplifying x = 5.565723957Subproblem 2
x + -1.224489796 = -4.341234161 Simplifying x + -1.224489796 = -4.341234161 Reorder the terms: -1.224489796 + x = -4.341234161 Solving -1.224489796 + x = -4.341234161 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.224489796' to each side of the equation. -1.224489796 + 1.224489796 + x = -4.341234161 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + x = -4.341234161 + 1.224489796 x = -4.341234161 + 1.224489796 Combine like terms: -4.341234161 + 1.224489796 = -3.116744365 x = -3.116744365 Simplifying x = -3.116744365Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.565723957, -3.116744365}
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