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Simplifying 2x2 + -43x + 143 = 0 Reorder the terms: 143 + -43x + 2x2 = 0 Solving 143 + -43x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 71.5 + -21.5x + x2 = 0 Move the constant term to the right: Add '-71.5' to each side of the equation. 71.5 + -21.5x + -71.5 + x2 = 0 + -71.5 Reorder the terms: 71.5 + -71.5 + -21.5x + x2 = 0 + -71.5 Combine like terms: 71.5 + -71.5 = 0.0 0.0 + -21.5x + x2 = 0 + -71.5 -21.5x + x2 = 0 + -71.5 Combine like terms: 0 + -71.5 = -71.5 -21.5x + x2 = -71.5 The x term is -21.5x. Take half its coefficient (-10.75). Square it (115.5625) and add it to both sides. Add '115.5625' to each side of the equation. -21.5x + 115.5625 + x2 = -71.5 + 115.5625 Reorder the terms: 115.5625 + -21.5x + x2 = -71.5 + 115.5625 Combine like terms: -71.5 + 115.5625 = 44.0625 115.5625 + -21.5x + x2 = 44.0625 Factor a perfect square on the left side: (x + -10.75)(x + -10.75) = 44.0625 Calculate the square root of the right side: 6.637959024 Break this problem into two subproblems by setting (x + -10.75) equal to 6.637959024 and -6.637959024.Subproblem 1
x + -10.75 = 6.637959024 Simplifying x + -10.75 = 6.637959024 Reorder the terms: -10.75 + x = 6.637959024 Solving -10.75 + x = 6.637959024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.75' to each side of the equation. -10.75 + 10.75 + x = 6.637959024 + 10.75 Combine like terms: -10.75 + 10.75 = 0.00 0.00 + x = 6.637959024 + 10.75 x = 6.637959024 + 10.75 Combine like terms: 6.637959024 + 10.75 = 17.387959024 x = 17.387959024 Simplifying x = 17.387959024Subproblem 2
x + -10.75 = -6.637959024 Simplifying x + -10.75 = -6.637959024 Reorder the terms: -10.75 + x = -6.637959024 Solving -10.75 + x = -6.637959024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.75' to each side of the equation. -10.75 + 10.75 + x = -6.637959024 + 10.75 Combine like terms: -10.75 + 10.75 = 0.00 0.00 + x = -6.637959024 + 10.75 x = -6.637959024 + 10.75 Combine like terms: -6.637959024 + 10.75 = 4.112040976 x = 4.112040976 Simplifying x = 4.112040976Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.387959024, 4.112040976}
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