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Simplifying 3x2 + -154x + 1120 = 0 Reorder the terms: 1120 + -154x + 3x2 = 0 Solving 1120 + -154x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 373.3333333 + -51.33333333x + x2 = 0 Move the constant term to the right: Add '-373.3333333' to each side of the equation. 373.3333333 + -51.33333333x + -373.3333333 + x2 = 0 + -373.3333333 Reorder the terms: 373.3333333 + -373.3333333 + -51.33333333x + x2 = 0 + -373.3333333 Combine like terms: 373.3333333 + -373.3333333 = 0.0000000 0.0000000 + -51.33333333x + x2 = 0 + -373.3333333 -51.33333333x + x2 = 0 + -373.3333333 Combine like terms: 0 + -373.3333333 = -373.3333333 -51.33333333x + x2 = -373.3333333 The x term is -51.33333333x. Take half its coefficient (-25.66666667). Square it (658.7777779) and add it to both sides. Add '658.7777779' to each side of the equation. -51.33333333x + 658.7777779 + x2 = -373.3333333 + 658.7777779 Reorder the terms: 658.7777779 + -51.33333333x + x2 = -373.3333333 + 658.7777779 Combine like terms: -373.3333333 + 658.7777779 = 285.4444446 658.7777779 + -51.33333333x + x2 = 285.4444446 Factor a perfect square on the left side: (x + -25.66666667)(x + -25.66666667) = 285.4444446 Calculate the square root of the right side: 16.895101201 Break this problem into two subproblems by setting (x + -25.66666667) equal to 16.895101201 and -16.895101201.Subproblem 1
x + -25.66666667 = 16.895101201 Simplifying x + -25.66666667 = 16.895101201 Reorder the terms: -25.66666667 + x = 16.895101201 Solving -25.66666667 + x = 16.895101201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25.66666667' to each side of the equation. -25.66666667 + 25.66666667 + x = 16.895101201 + 25.66666667 Combine like terms: -25.66666667 + 25.66666667 = 0.00000000 0.00000000 + x = 16.895101201 + 25.66666667 x = 16.895101201 + 25.66666667 Combine like terms: 16.895101201 + 25.66666667 = 42.561767871 x = 42.561767871 Simplifying x = 42.561767871Subproblem 2
x + -25.66666667 = -16.895101201 Simplifying x + -25.66666667 = -16.895101201 Reorder the terms: -25.66666667 + x = -16.895101201 Solving -25.66666667 + x = -16.895101201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25.66666667' to each side of the equation. -25.66666667 + 25.66666667 + x = -16.895101201 + 25.66666667 Combine like terms: -25.66666667 + 25.66666667 = 0.00000000 0.00000000 + x = -16.895101201 + 25.66666667 x = -16.895101201 + 25.66666667 Combine like terms: -16.895101201 + 25.66666667 = 8.771565469 x = 8.771565469 Simplifying x = 8.771565469Solution
The solution to the problem is based on the solutions from the subproblems. x = {42.561767871, 8.771565469}
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