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Simplifying 0 = 305 + 60.23x + -4.9x2 Solving 0 = 305 + 60.23x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -305 = -305 -305 + -60.23x + 4.9x2 = 305 + 60.23x + -4.9x2 + -305 + -60.23x + 4.9x2 Reorder the terms: -305 + -60.23x + 4.9x2 = 305 + -305 + 60.23x + -60.23x + -4.9x2 + 4.9x2 Combine like terms: 305 + -305 = 0 -305 + -60.23x + 4.9x2 = 0 + 60.23x + -60.23x + -4.9x2 + 4.9x2 -305 + -60.23x + 4.9x2 = 60.23x + -60.23x + -4.9x2 + 4.9x2 Combine like terms: 60.23x + -60.23x = 0.00 -305 + -60.23x + 4.9x2 = 0.00 + -4.9x2 + 4.9x2 -305 + -60.23x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -305 + -60.23x + 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'. -62.24489796 + -12.29183673x + x2 = 0 Move the constant term to the right: Add '62.24489796' to each side of the equation. -62.24489796 + -12.29183673x + 62.24489796 + x2 = 0 + 62.24489796 Reorder the terms: -62.24489796 + 62.24489796 + -12.29183673x + x2 = 0 + 62.24489796 Combine like terms: -62.24489796 + 62.24489796 = 0.00000000 0.00000000 + -12.29183673x + x2 = 0 + 62.24489796 -12.29183673x + x2 = 0 + 62.24489796 Combine like terms: 0 + 62.24489796 = 62.24489796 -12.29183673x + x2 = 62.24489796 The x term is -12.29183673x. Take half its coefficient (-6.145918365). Square it (37.77231255) and add it to both sides. Add '37.77231255' to each side of the equation. -12.29183673x + 37.77231255 + x2 = 62.24489796 + 37.77231255 Reorder the terms: 37.77231255 + -12.29183673x + x2 = 62.24489796 + 37.77231255 Combine like terms: 62.24489796 + 37.77231255 = 100.01721051 37.77231255 + -12.29183673x + x2 = 100.01721051 Factor a perfect square on the left side: (x + -6.145918365)(x + -6.145918365) = 100.01721051 Calculate the square root of the right side: 10.000860488 Break this problem into two subproblems by setting (x + -6.145918365) equal to 10.000860488 and -10.000860488.Subproblem 1
x + -6.145918365 = 10.000860488 Simplifying x + -6.145918365 = 10.000860488 Reorder the terms: -6.145918365 + x = 10.000860488 Solving -6.145918365 + x = 10.000860488 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.145918365' to each side of the equation. -6.145918365 + 6.145918365 + x = 10.000860488 + 6.145918365 Combine like terms: -6.145918365 + 6.145918365 = 0.000000000 0.000000000 + x = 10.000860488 + 6.145918365 x = 10.000860488 + 6.145918365 Combine like terms: 10.000860488 + 6.145918365 = 16.146778853 x = 16.146778853 Simplifying x = 16.146778853Subproblem 2
x + -6.145918365 = -10.000860488 Simplifying x + -6.145918365 = -10.000860488 Reorder the terms: -6.145918365 + x = -10.000860488 Solving -6.145918365 + x = -10.000860488 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.145918365' to each side of the equation. -6.145918365 + 6.145918365 + x = -10.000860488 + 6.145918365 Combine like terms: -6.145918365 + 6.145918365 = 0.000000000 0.000000000 + x = -10.000860488 + 6.145918365 x = -10.000860488 + 6.145918365 Combine like terms: -10.000860488 + 6.145918365 = -3.854942123 x = -3.854942123 Simplifying x = -3.854942123Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.146778853, -3.854942123}
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