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Simplifying 198 = 2x2 + -7x Reorder the terms: 198 = -7x + 2x2 Solving 198 = -7x + 2x2 Solving for variable 'x'. Reorder the terms: 198 + 7x + -2x2 = -7x + 7x + 2x2 + -2x2 Combine like terms: -7x + 7x = 0 198 + 7x + -2x2 = 0 + 2x2 + -2x2 198 + 7x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 198 + 7x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -99 + -3.5x + x2 = 0 Move the constant term to the right: Add '99' to each side of the equation. -99 + -3.5x + 99 + x2 = 0 + 99 Reorder the terms: -99 + 99 + -3.5x + x2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + -3.5x + x2 = 0 + 99 -3.5x + x2 = 0 + 99 Combine like terms: 0 + 99 = 99 -3.5x + x2 = 99 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 99 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 99 + 3.0625 Combine like terms: 99 + 3.0625 = 102.0625 3.0625 + -3.5x + x2 = 102.0625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 102.0625 Calculate the square root of the right side: 10.102598676 Break this problem into two subproblems by setting (x + -1.75) equal to 10.102598676 and -10.102598676.Subproblem 1
x + -1.75 = 10.102598676 Simplifying x + -1.75 = 10.102598676 Reorder the terms: -1.75 + x = 10.102598676 Solving -1.75 + x = 10.102598676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 10.102598676 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 10.102598676 + 1.75 x = 10.102598676 + 1.75 Combine like terms: 10.102598676 + 1.75 = 11.852598676 x = 11.852598676 Simplifying x = 11.852598676Subproblem 2
x + -1.75 = -10.102598676 Simplifying x + -1.75 = -10.102598676 Reorder the terms: -1.75 + x = -10.102598676 Solving -1.75 + x = -10.102598676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -10.102598676 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -10.102598676 + 1.75 x = -10.102598676 + 1.75 Combine like terms: -10.102598676 + 1.75 = -8.352598676 x = -8.352598676 Simplifying x = -8.352598676Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.852598676, -8.352598676}
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