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Simplifying 12x + 4.9x2 = 5 Solving 12x + 4.9x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 12x + 4.9x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 12x + 4.9x2 = 0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -1.020408163 + 2.448979592x + x2 = 0 Move the constant term to the right: Add '1.020408163' to each side of the equation. -1.020408163 + 2.448979592x + 1.020408163 + x2 = 0 + 1.020408163 Reorder the terms: -1.020408163 + 1.020408163 + 2.448979592x + x2 = 0 + 1.020408163 Combine like terms: -1.020408163 + 1.020408163 = 0.000000000 0.000000000 + 2.448979592x + x2 = 0 + 1.020408163 2.448979592x + x2 = 0 + 1.020408163 Combine like terms: 0 + 1.020408163 = 1.020408163 2.448979592x + x2 = 1.020408163 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 = 1.020408163 + 1.499375261 Reorder the terms: 1.499375261 + 2.448979592x + x2 = 1.020408163 + 1.499375261 Combine like terms: 1.020408163 + 1.499375261 = 2.519783424 1.499375261 + 2.448979592x + x2 = 2.519783424 Factor a perfect square on the left side: (x + 1.224489796)(x + 1.224489796) = 2.519783424 Calculate the square root of the right side: 1.58738257 Break this problem into two subproblems by setting (x + 1.224489796) equal to 1.58738257 and -1.58738257.Subproblem 1
x + 1.224489796 = 1.58738257 Simplifying x + 1.224489796 = 1.58738257 Reorder the terms: 1.224489796 + x = 1.58738257 Solving 1.224489796 + x = 1.58738257 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 = 1.58738257 + -1.224489796 Combine like terms: 1.224489796 + -1.224489796 = 0.000000000 0.000000000 + x = 1.58738257 + -1.224489796 x = 1.58738257 + -1.224489796 Combine like terms: 1.58738257 + -1.224489796 = 0.362892774 x = 0.362892774 Simplifying x = 0.362892774Subproblem 2
x + 1.224489796 = -1.58738257 Simplifying x + 1.224489796 = -1.58738257 Reorder the terms: 1.224489796 + x = -1.58738257 Solving 1.224489796 + x = -1.58738257 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 = -1.58738257 + -1.224489796 Combine like terms: 1.224489796 + -1.224489796 = 0.000000000 0.000000000 + x = -1.58738257 + -1.224489796 x = -1.58738257 + -1.224489796 Combine like terms: -1.58738257 + -1.224489796 = -2.811872366 x = -2.811872366 Simplifying x = -2.811872366Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.362892774, -2.811872366}
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