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Simplifying 9x2 + 11x + 30.25 = 33.25 Reorder the terms: 30.25 + 11x + 9x2 = 33.25 Solving 30.25 + 11x + 9x2 = 33.25 Solving for variable 'x'. Reorder the terms: 30.25 + -33.25 + 11x + 9x2 = 33.25 + -33.25 Combine like terms: 30.25 + -33.25 = -3 -3 + 11x + 9x2 = 33.25 + -33.25 Combine like terms: 33.25 + -33.25 = 0.00 -3 + 11x + 9x2 = 0.00 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.3333333333 + 1.222222222x + x2 = 0.00 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 1.222222222x + 0.3333333333 + x2 = 0.00 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 1.222222222x + x2 = 0.00 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 1.222222222x + x2 = 0.00 + 0.3333333333 1.222222222x + x2 = 0.00 + 0.3333333333 Combine like terms: 0.00 + 0.3333333333 = 0.3333333333 1.222222222x + x2 = 0.3333333333 The x term is 1.222222222x. Take half its coefficient (0.611111111). Square it (0.3734567900) and add it to both sides. Add '0.3734567900' to each side of the equation. 1.222222222x + 0.3734567900 + x2 = 0.3333333333 + 0.3734567900 Reorder the terms: 0.3734567900 + 1.222222222x + x2 = 0.3333333333 + 0.3734567900 Combine like terms: 0.3333333333 + 0.3734567900 = 0.7067901233 0.3734567900 + 1.222222222x + x2 = 0.7067901233 Factor a perfect square on the left side: (x + 0.611111111)(x + 0.611111111) = 0.7067901233 Calculate the square root of the right side: 0.840708108 Break this problem into two subproblems by setting (x + 0.611111111) equal to 0.840708108 and -0.840708108.Subproblem 1
x + 0.611111111 = 0.840708108 Simplifying x + 0.611111111 = 0.840708108 Reorder the terms: 0.611111111 + x = 0.840708108 Solving 0.611111111 + x = 0.840708108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.611111111' to each side of the equation. 0.611111111 + -0.611111111 + x = 0.840708108 + -0.611111111 Combine like terms: 0.611111111 + -0.611111111 = 0.000000000 0.000000000 + x = 0.840708108 + -0.611111111 x = 0.840708108 + -0.611111111 Combine like terms: 0.840708108 + -0.611111111 = 0.229596997 x = 0.229596997 Simplifying x = 0.229596997Subproblem 2
x + 0.611111111 = -0.840708108 Simplifying x + 0.611111111 = -0.840708108 Reorder the terms: 0.611111111 + x = -0.840708108 Solving 0.611111111 + x = -0.840708108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.611111111' to each side of the equation. 0.611111111 + -0.611111111 + x = -0.840708108 + -0.611111111 Combine like terms: 0.611111111 + -0.611111111 = 0.000000000 0.000000000 + x = -0.840708108 + -0.611111111 x = -0.840708108 + -0.611111111 Combine like terms: -0.840708108 + -0.611111111 = -1.451819219 x = -1.451819219 Simplifying x = -1.451819219Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.229596997, -1.451819219}
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