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Simplifying -4.9x2 + 12x + 500 = 0 Reorder the terms: 500 + 12x + -4.9x2 = 0 Solving 500 + 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'. -102.0408163 + -2.448979592x + x2 = 0 Move the constant term to the right: Add '102.0408163' to each side of the equation. -102.0408163 + -2.448979592x + 102.0408163 + x2 = 0 + 102.0408163 Reorder the terms: -102.0408163 + 102.0408163 + -2.448979592x + x2 = 0 + 102.0408163 Combine like terms: -102.0408163 + 102.0408163 = 0.0000000 0.0000000 + -2.448979592x + x2 = 0 + 102.0408163 -2.448979592x + x2 = 0 + 102.0408163 Combine like terms: 0 + 102.0408163 = 102.0408163 -2.448979592x + x2 = 102.0408163 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 = 102.0408163 + 1.499375261 Reorder the terms: 1.499375261 + -2.448979592x + x2 = 102.0408163 + 1.499375261 Combine like terms: 102.0408163 + 1.499375261 = 103.540191561 1.499375261 + -2.448979592x + x2 = 103.540191561 Factor a perfect square on the left side: (x + -1.224489796)(x + -1.224489796) = 103.540191561 Calculate the square root of the right side: 10.17547009 Break this problem into two subproblems by setting (x + -1.224489796) equal to 10.17547009 and -10.17547009.Subproblem 1
x + -1.224489796 = 10.17547009 Simplifying x + -1.224489796 = 10.17547009 Reorder the terms: -1.224489796 + x = 10.17547009 Solving -1.224489796 + x = 10.17547009 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 = 10.17547009 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + x = 10.17547009 + 1.224489796 x = 10.17547009 + 1.224489796 Combine like terms: 10.17547009 + 1.224489796 = 11.399959886 x = 11.399959886 Simplifying x = 11.399959886Subproblem 2
x + -1.224489796 = -10.17547009 Simplifying x + -1.224489796 = -10.17547009 Reorder the terms: -1.224489796 + x = -10.17547009 Solving -1.224489796 + x = -10.17547009 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 = -10.17547009 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + x = -10.17547009 + 1.224489796 x = -10.17547009 + 1.224489796 Combine like terms: -10.17547009 + 1.224489796 = -8.950980294 x = -8.950980294 Simplifying x = -8.950980294Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.399959886, -8.950980294}
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