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Simplifying 2x2 + -55x + 80 = 0 Reorder the terms: 80 + -55x + 2x2 = 0 Solving 80 + -55x + 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'. 40 + -27.5x + x2 = 0 Move the constant term to the right: Add '-40' to each side of the equation. 40 + -27.5x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + -27.5x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -27.5x + x2 = 0 + -40 -27.5x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 -27.5x + x2 = -40 The x term is -27.5x. Take half its coefficient (-13.75). Square it (189.0625) and add it to both sides. Add '189.0625' to each side of the equation. -27.5x + 189.0625 + x2 = -40 + 189.0625 Reorder the terms: 189.0625 + -27.5x + x2 = -40 + 189.0625 Combine like terms: -40 + 189.0625 = 149.0625 189.0625 + -27.5x + x2 = 149.0625 Factor a perfect square on the left side: (x + -13.75)(x + -13.75) = 149.0625 Calculate the square root of the right side: 12.209115447 Break this problem into two subproblems by setting (x + -13.75) equal to 12.209115447 and -12.209115447.Subproblem 1
x + -13.75 = 12.209115447 Simplifying x + -13.75 = 12.209115447 Reorder the terms: -13.75 + x = 12.209115447 Solving -13.75 + x = 12.209115447 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.75' to each side of the equation. -13.75 + 13.75 + x = 12.209115447 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + x = 12.209115447 + 13.75 x = 12.209115447 + 13.75 Combine like terms: 12.209115447 + 13.75 = 25.959115447 x = 25.959115447 Simplifying x = 25.959115447Subproblem 2
x + -13.75 = -12.209115447 Simplifying x + -13.75 = -12.209115447 Reorder the terms: -13.75 + x = -12.209115447 Solving -13.75 + x = -12.209115447 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.75' to each side of the equation. -13.75 + 13.75 + x = -12.209115447 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + x = -12.209115447 + 13.75 x = -12.209115447 + 13.75 Combine like terms: -12.209115447 + 13.75 = 1.540884553 x = 1.540884553 Simplifying x = 1.540884553Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.959115447, 1.540884553}
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