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Simplifying -3x2 + 299x + -325 = 0 Reorder the terms: -325 + 299x + -3x2 = 0 Solving -325 + 299x + -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'. 108.3333333 + -99.66666667x + x2 = 0 Move the constant term to the right: Add '-108.3333333' to each side of the equation. 108.3333333 + -99.66666667x + -108.3333333 + x2 = 0 + -108.3333333 Reorder the terms: 108.3333333 + -108.3333333 + -99.66666667x + x2 = 0 + -108.3333333 Combine like terms: 108.3333333 + -108.3333333 = 0.0000000 0.0000000 + -99.66666667x + x2 = 0 + -108.3333333 -99.66666667x + x2 = 0 + -108.3333333 Combine like terms: 0 + -108.3333333 = -108.3333333 -99.66666667x + x2 = -108.3333333 The x term is -99.66666667x. Take half its coefficient (-49.83333334). Square it (2483.361112) and add it to both sides. Add '2483.361112' to each side of the equation. -99.66666667x + 2483.361112 + x2 = -108.3333333 + 2483.361112 Reorder the terms: 2483.361112 + -99.66666667x + x2 = -108.3333333 + 2483.361112 Combine like terms: -108.3333333 + 2483.361112 = 2375.0277787 2483.361112 + -99.66666667x + x2 = 2375.0277787 Factor a perfect square on the left side: (x + -49.83333334)(x + -49.83333334) = 2375.0277787 Calculate the square root of the right side: 48.734256727 Break this problem into two subproblems by setting (x + -49.83333334) equal to 48.734256727 and -48.734256727.Subproblem 1
x + -49.83333334 = 48.734256727 Simplifying x + -49.83333334 = 48.734256727 Reorder the terms: -49.83333334 + x = 48.734256727 Solving -49.83333334 + x = 48.734256727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '49.83333334' to each side of the equation. -49.83333334 + 49.83333334 + x = 48.734256727 + 49.83333334 Combine like terms: -49.83333334 + 49.83333334 = 0.00000000 0.00000000 + x = 48.734256727 + 49.83333334 x = 48.734256727 + 49.83333334 Combine like terms: 48.734256727 + 49.83333334 = 98.567590067 x = 98.567590067 Simplifying x = 98.567590067Subproblem 2
x + -49.83333334 = -48.734256727 Simplifying x + -49.83333334 = -48.734256727 Reorder the terms: -49.83333334 + x = -48.734256727 Solving -49.83333334 + x = -48.734256727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '49.83333334' to each side of the equation. -49.83333334 + 49.83333334 + x = -48.734256727 + 49.83333334 Combine like terms: -49.83333334 + 49.83333334 = 0.00000000 0.00000000 + x = -48.734256727 + 49.83333334 x = -48.734256727 + 49.83333334 Combine like terms: -48.734256727 + 49.83333334 = 1.099076613 x = 1.099076613 Simplifying x = 1.099076613Solution
The solution to the problem is based on the solutions from the subproblems. x = {98.567590067, 1.099076613}
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