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Simplifying 5 = 12x + -4.9x2 Solving 5 = 12x + -4.9x2 Solving for variable 'x'. Reorder the terms: 5 + -12x + 4.9x2 = 12x + -12x + -4.9x2 + 4.9x2 Combine like terms: 12x + -12x = 0 5 + -12x + 4.9x2 = 0 + -4.9x2 + 4.9x2 5 + -12x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 5 + -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'. 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 = 0.478967098 1.499375261 + -2.448979592x + x2 = 0.478967098 Factor a perfect square on the left side: (x + -1.224489796)(x + -1.224489796) = 0.478967098 Calculate the square root of the right side: 0.692074489 Break this problem into two subproblems by setting (x + -1.224489796) equal to 0.692074489 and -0.692074489.Subproblem 1
x + -1.224489796 = 0.692074489 Simplifying x + -1.224489796 = 0.692074489 Reorder the terms: -1.224489796 + x = 0.692074489 Solving -1.224489796 + x = 0.692074489 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 = 0.692074489 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + x = 0.692074489 + 1.224489796 x = 0.692074489 + 1.224489796 Combine like terms: 0.692074489 + 1.224489796 = 1.916564285 x = 1.916564285 Simplifying x = 1.916564285Subproblem 2
x + -1.224489796 = -0.692074489 Simplifying x + -1.224489796 = -0.692074489 Reorder the terms: -1.224489796 + x = -0.692074489 Solving -1.224489796 + x = -0.692074489 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 = -0.692074489 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + x = -0.692074489 + 1.224489796 x = -0.692074489 + 1.224489796 Combine like terms: -0.692074489 + 1.224489796 = 0.532415307 x = 0.532415307 Simplifying x = 0.532415307Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.916564285, 0.532415307}
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