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Simplifying 0 = 4.9x2 + 12x + -80 Reorder the terms: 0 = -80 + 12x + 4.9x2 Solving 0 = -80 + 12x + 4.9x2 Solving for variable 'x'. Combine like terms: 0 + 80 = 80 80 + -12x + -4.9x2 = -80 + 12x + 4.9x2 + 80 + -12x + -4.9x2 Reorder the terms: 80 + -12x + -4.9x2 = -80 + 80 + 12x + -12x + 4.9x2 + -4.9x2 Combine like terms: -80 + 80 = 0 80 + -12x + -4.9x2 = 0 + 12x + -12x + 4.9x2 + -4.9x2 80 + -12x + -4.9x2 = 12x + -12x + 4.9x2 + -4.9x2 Combine like terms: 12x + -12x = 0 80 + -12x + -4.9x2 = 0 + 4.9x2 + -4.9x2 80 + -12x + -4.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 80 + -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'. -16.32653061 + 2.448979592x + x2 = 0 Move the constant term to the right: Add '16.32653061' to each side of the equation. -16.32653061 + 2.448979592x + 16.32653061 + x2 = 0 + 16.32653061 Reorder the terms: -16.32653061 + 16.32653061 + 2.448979592x + x2 = 0 + 16.32653061 Combine like terms: -16.32653061 + 16.32653061 = 0.00000000 0.00000000 + 2.448979592x + x2 = 0 + 16.32653061 2.448979592x + x2 = 0 + 16.32653061 Combine like terms: 0 + 16.32653061 = 16.32653061 2.448979592x + x2 = 16.32653061 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 = 16.32653061 + 1.499375261 Reorder the terms: 1.499375261 + 2.448979592x + x2 = 16.32653061 + 1.499375261 Combine like terms: 16.32653061 + 1.499375261 = 17.825905871 1.499375261 + 2.448979592x + x2 = 17.825905871 Factor a perfect square on the left side: (x + 1.224489796)(x + 1.224489796) = 17.825905871 Calculate the square root of the right side: 4.222073646 Break this problem into two subproblems by setting (x + 1.224489796) equal to 4.222073646 and -4.222073646.Subproblem 1
x + 1.224489796 = 4.222073646 Simplifying x + 1.224489796 = 4.222073646 Reorder the terms: 1.224489796 + x = 4.222073646 Solving 1.224489796 + x = 4.222073646 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 = 4.222073646 + -1.224489796 Combine like terms: 1.224489796 + -1.224489796 = 0.000000000 0.000000000 + x = 4.222073646 + -1.224489796 x = 4.222073646 + -1.224489796 Combine like terms: 4.222073646 + -1.224489796 = 2.99758385 x = 2.99758385 Simplifying x = 2.99758385Subproblem 2
x + 1.224489796 = -4.222073646 Simplifying x + 1.224489796 = -4.222073646 Reorder the terms: 1.224489796 + x = -4.222073646 Solving 1.224489796 + x = -4.222073646 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 = -4.222073646 + -1.224489796 Combine like terms: 1.224489796 + -1.224489796 = 0.000000000 0.000000000 + x = -4.222073646 + -1.224489796 x = -4.222073646 + -1.224489796 Combine like terms: -4.222073646 + -1.224489796 = -5.446563442 x = -5.446563442 Simplifying x = -5.446563442Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.99758385, -5.446563442}
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