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Simplifying 4.9x2 + -120x = -100 Reorder the terms: -120x + 4.9x2 = -100 Solving -120x + 4.9x2 = -100 Solving for variable 'x'. Reorder the terms: 100 + -120x + 4.9x2 = -100 + 100 Combine like terms: -100 + 100 = 0 100 + -120x + 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'. 20.40816327 + -24.48979592x + x2 = 0 Move the constant term to the right: Add '-20.40816327' to each side of the equation. 20.40816327 + -24.48979592x + -20.40816327 + x2 = 0 + -20.40816327 Reorder the terms: 20.40816327 + -20.40816327 + -24.48979592x + x2 = 0 + -20.40816327 Combine like terms: 20.40816327 + -20.40816327 = 0.00000000 0.00000000 + -24.48979592x + x2 = 0 + -20.40816327 -24.48979592x + x2 = 0 + -20.40816327 Combine like terms: 0 + -20.40816327 = -20.40816327 -24.48979592x + x2 = -20.40816327 The x term is -24.48979592x. Take half its coefficient (-12.24489796). Square it (149.9375261) and add it to both sides. Add '149.9375261' to each side of the equation. -24.48979592x + 149.9375261 + x2 = -20.40816327 + 149.9375261 Reorder the terms: 149.9375261 + -24.48979592x + x2 = -20.40816327 + 149.9375261 Combine like terms: -20.40816327 + 149.9375261 = 129.52936283 149.9375261 + -24.48979592x + x2 = 129.52936283 Factor a perfect square on the left side: (x + -12.24489796)(x + -12.24489796) = 129.52936283 Calculate the square root of the right side: 11.381096732 Break this problem into two subproblems by setting (x + -12.24489796) equal to 11.381096732 and -11.381096732.Subproblem 1
x + -12.24489796 = 11.381096732 Simplifying x + -12.24489796 = 11.381096732 Reorder the terms: -12.24489796 + x = 11.381096732 Solving -12.24489796 + x = 11.381096732 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.24489796' to each side of the equation. -12.24489796 + 12.24489796 + x = 11.381096732 + 12.24489796 Combine like terms: -12.24489796 + 12.24489796 = 0.00000000 0.00000000 + x = 11.381096732 + 12.24489796 x = 11.381096732 + 12.24489796 Combine like terms: 11.381096732 + 12.24489796 = 23.625994692 x = 23.625994692 Simplifying x = 23.625994692Subproblem 2
x + -12.24489796 = -11.381096732 Simplifying x + -12.24489796 = -11.381096732 Reorder the terms: -12.24489796 + x = -11.381096732 Solving -12.24489796 + x = -11.381096732 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.24489796' to each side of the equation. -12.24489796 + 12.24489796 + x = -11.381096732 + 12.24489796 Combine like terms: -12.24489796 + 12.24489796 = 0.00000000 0.00000000 + x = -11.381096732 + 12.24489796 x = -11.381096732 + 12.24489796 Combine like terms: -11.381096732 + 12.24489796 = 0.863801228 x = 0.863801228 Simplifying x = 0.863801228Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.625994692, 0.863801228}
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