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Simplifying 153.9x2 + -175.9x + 50.2 = 0 Reorder the terms: 50.2 + -175.9x + 153.9x2 = 0 Solving 50.2 + -175.9x + 153.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 153.9 the coefficient of the squared term: Divide each side by '153.9'. 0.326185835 + -1.142949968x + x2 = 0 Move the constant term to the right: Add '-0.326185835' to each side of the equation. 0.326185835 + -1.142949968x + -0.326185835 + x2 = 0 + -0.326185835 Reorder the terms: 0.326185835 + -0.326185835 + -1.142949968x + x2 = 0 + -0.326185835 Combine like terms: 0.326185835 + -0.326185835 = 0.000000000 0.000000000 + -1.142949968x + x2 = 0 + -0.326185835 -1.142949968x + x2 = 0 + -0.326185835 Combine like terms: 0 + -0.326185835 = -0.326185835 -1.142949968x + x2 = -0.326185835 The x term is -1.142949968x. Take half its coefficient (-0.571474984). Square it (0.3265836573) and add it to both sides. Add '0.3265836573' to each side of the equation. -1.142949968x + 0.3265836573 + x2 = -0.326185835 + 0.3265836573 Reorder the terms: 0.3265836573 + -1.142949968x + x2 = -0.326185835 + 0.3265836573 Combine like terms: -0.326185835 + 0.3265836573 = 0.0003978223 0.3265836573 + -1.142949968x + x2 = 0.0003978223 Factor a perfect square on the left side: (x + -0.571474984)(x + -0.571474984) = 0.0003978223 Calculate the square root of the right side: 0.019945483 Break this problem into two subproblems by setting (x + -0.571474984) equal to 0.019945483 and -0.019945483.Subproblem 1
x + -0.571474984 = 0.019945483 Simplifying x + -0.571474984 = 0.019945483 Reorder the terms: -0.571474984 + x = 0.019945483 Solving -0.571474984 + x = 0.019945483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.571474984' to each side of the equation. -0.571474984 + 0.571474984 + x = 0.019945483 + 0.571474984 Combine like terms: -0.571474984 + 0.571474984 = 0.000000000 0.000000000 + x = 0.019945483 + 0.571474984 x = 0.019945483 + 0.571474984 Combine like terms: 0.019945483 + 0.571474984 = 0.591420467 x = 0.591420467 Simplifying x = 0.591420467Subproblem 2
x + -0.571474984 = -0.019945483 Simplifying x + -0.571474984 = -0.019945483 Reorder the terms: -0.571474984 + x = -0.019945483 Solving -0.571474984 + x = -0.019945483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.571474984' to each side of the equation. -0.571474984 + 0.571474984 + x = -0.019945483 + 0.571474984 Combine like terms: -0.571474984 + 0.571474984 = 0.000000000 0.000000000 + x = -0.019945483 + 0.571474984 x = -0.019945483 + 0.571474984 Combine like terms: -0.019945483 + 0.571474984 = 0.551529501 x = 0.551529501 Simplifying x = 0.551529501Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.591420467, 0.551529501}
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