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Simplifying -4.9x2 + 12x + -0.8 = 0 Reorder the terms: -0.8 + 12x + -4.9x2 = 0 Solving -0.8 + 12x + -4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. 0.1632653061 + -2.448979592x + x2 = 0 Move the constant term to the right: Add '-0.1632653061' to each side of the equation. 0.1632653061 + -2.448979592x + -0.1632653061 + x2 = 0 + -0.1632653061 Reorder the terms: 0.1632653061 + -0.1632653061 + -2.448979592x + x2 = 0 + -0.1632653061 Combine like terms: 0.1632653061 + -0.1632653061 = 0.0000000000 0.0000000000 + -2.448979592x + x2 = 0 + -0.1632653061 -2.448979592x + x2 = 0 + -0.1632653061 Combine like terms: 0 + -0.1632653061 = -0.1632653061 -2.448979592x + x2 = -0.1632653061 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 = -0.1632653061 + 1.499375261 Reorder the terms: 1.499375261 + -2.448979592x + x2 = -0.1632653061 + 1.499375261 Combine like terms: -0.1632653061 + 1.499375261 = 1.3361099549 1.499375261 + -2.448979592x + x2 = 1.3361099549 Factor a perfect square on the left side: (x + -1.224489796)(x + -1.224489796) = 1.3361099549 Calculate the square root of the right side: 1.155902225 Break this problem into two subproblems by setting (x + -1.224489796) equal to 1.155902225 and -1.155902225.Subproblem 1
x + -1.224489796 = 1.155902225 Simplifying x + -1.224489796 = 1.155902225 Reorder the terms: -1.224489796 + x = 1.155902225 Solving -1.224489796 + x = 1.155902225 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 = 1.155902225 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + x = 1.155902225 + 1.224489796 x = 1.155902225 + 1.224489796 Combine like terms: 1.155902225 + 1.224489796 = 2.380392021 x = 2.380392021 Simplifying x = 2.380392021Subproblem 2
x + -1.224489796 = -1.155902225 Simplifying x + -1.224489796 = -1.155902225 Reorder the terms: -1.224489796 + x = -1.155902225 Solving -1.224489796 + x = -1.155902225 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 = -1.155902225 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + x = -1.155902225 + 1.224489796 x = -1.155902225 + 1.224489796 Combine like terms: -1.155902225 + 1.224489796 = 0.068587571 x = 0.068587571 Simplifying x = 0.068587571Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.380392021, 0.068587571}
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