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Simplifying 91 = 2x2 + 3x + 2 Reorder the terms: 91 = 2 + 3x + 2x2 Solving 91 = 2 + 3x + 2x2 Solving for variable 'x'. Combine like terms: 91 + -2 = 89 89 + -3x + -2x2 = 2 + 3x + 2x2 + -2 + -3x + -2x2 Reorder the terms: 89 + -3x + -2x2 = 2 + -2 + 3x + -3x + 2x2 + -2x2 Combine like terms: 2 + -2 = 0 89 + -3x + -2x2 = 0 + 3x + -3x + 2x2 + -2x2 89 + -3x + -2x2 = 3x + -3x + 2x2 + -2x2 Combine like terms: 3x + -3x = 0 89 + -3x + -2x2 = 0 + 2x2 + -2x2 89 + -3x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 89 + -3x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -44.5 + 1.5x + x2 = 0 Move the constant term to the right: Add '44.5' to each side of the equation. -44.5 + 1.5x + 44.5 + x2 = 0 + 44.5 Reorder the terms: -44.5 + 44.5 + 1.5x + x2 = 0 + 44.5 Combine like terms: -44.5 + 44.5 = 0.0 0.0 + 1.5x + x2 = 0 + 44.5 1.5x + x2 = 0 + 44.5 Combine like terms: 0 + 44.5 = 44.5 1.5x + x2 = 44.5 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 44.5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 44.5 + 0.5625 Combine like terms: 44.5 + 0.5625 = 45.0625 0.5625 + 1.5x + x2 = 45.0625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 45.0625 Calculate the square root of the right side: 6.712860791 Break this problem into two subproblems by setting (x + 0.75) equal to 6.712860791 and -6.712860791.Subproblem 1
x + 0.75 = 6.712860791 Simplifying x + 0.75 = 6.712860791 Reorder the terms: 0.75 + x = 6.712860791 Solving 0.75 + x = 6.712860791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 6.712860791 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 6.712860791 + -0.75 x = 6.712860791 + -0.75 Combine like terms: 6.712860791 + -0.75 = 5.962860791 x = 5.962860791 Simplifying x = 5.962860791Subproblem 2
x + 0.75 = -6.712860791 Simplifying x + 0.75 = -6.712860791 Reorder the terms: 0.75 + x = -6.712860791 Solving 0.75 + x = -6.712860791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -6.712860791 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -6.712860791 + -0.75 x = -6.712860791 + -0.75 Combine like terms: -6.712860791 + -0.75 = -7.462860791 x = -7.462860791 Simplifying x = -7.462860791Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.962860791, -7.462860791}
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