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Simplifying (4x2 + 9x) + (9x2 + -7x + -73) = 0 Reorder the terms: (9x + 4x2) + (9x2 + -7x + -73) = 0 Remove parenthesis around (9x + 4x2) 9x + 4x2 + (9x2 + -7x + -73) = 0 Reorder the terms: 9x + 4x2 + (-73 + -7x + 9x2) = 0 Remove parenthesis around (-73 + -7x + 9x2) 9x + 4x2 + -73 + -7x + 9x2 = 0 Reorder the terms: -73 + 9x + -7x + 4x2 + 9x2 = 0 Combine like terms: 9x + -7x = 2x -73 + 2x + 4x2 + 9x2 = 0 Combine like terms: 4x2 + 9x2 = 13x2 -73 + 2x + 13x2 = 0 Solving -73 + 2x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -5.615384615 + 0.1538461538x + x2 = 0 Move the constant term to the right: Add '5.615384615' to each side of the equation. -5.615384615 + 0.1538461538x + 5.615384615 + x2 = 0 + 5.615384615 Reorder the terms: -5.615384615 + 5.615384615 + 0.1538461538x + x2 = 0 + 5.615384615 Combine like terms: -5.615384615 + 5.615384615 = 0.000000000 0.000000000 + 0.1538461538x + x2 = 0 + 5.615384615 0.1538461538x + x2 = 0 + 5.615384615 Combine like terms: 0 + 5.615384615 = 5.615384615 0.1538461538x + x2 = 5.615384615 The x term is 0.1538461538x. Take half its coefficient (0.0769230769). Square it (0.005917159760) and add it to both sides. Add '0.005917159760' to each side of the equation. 0.1538461538x + 0.005917159760 + x2 = 5.615384615 + 0.005917159760 Reorder the terms: 0.005917159760 + 0.1538461538x + x2 = 5.615384615 + 0.005917159760 Combine like terms: 5.615384615 + 0.005917159760 = 5.62130177476 0.005917159760 + 0.1538461538x + x2 = 5.62130177476 Factor a perfect square on the left side: (x + 0.0769230769)(x + 0.0769230769) = 5.62130177476 Calculate the square root of the right side: 2.370928463 Break this problem into two subproblems by setting (x + 0.0769230769) equal to 2.370928463 and -2.370928463.Subproblem 1
x + 0.0769230769 = 2.370928463 Simplifying x + 0.0769230769 = 2.370928463 Reorder the terms: 0.0769230769 + x = 2.370928463 Solving 0.0769230769 + x = 2.370928463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0769230769' to each side of the equation. 0.0769230769 + -0.0769230769 + x = 2.370928463 + -0.0769230769 Combine like terms: 0.0769230769 + -0.0769230769 = 0.0000000000 0.0000000000 + x = 2.370928463 + -0.0769230769 x = 2.370928463 + -0.0769230769 Combine like terms: 2.370928463 + -0.0769230769 = 2.2940053861 x = 2.2940053861 Simplifying x = 2.2940053861Subproblem 2
x + 0.0769230769 = -2.370928463 Simplifying x + 0.0769230769 = -2.370928463 Reorder the terms: 0.0769230769 + x = -2.370928463 Solving 0.0769230769 + x = -2.370928463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0769230769' to each side of the equation. 0.0769230769 + -0.0769230769 + x = -2.370928463 + -0.0769230769 Combine like terms: 0.0769230769 + -0.0769230769 = 0.0000000000 0.0000000000 + x = -2.370928463 + -0.0769230769 x = -2.370928463 + -0.0769230769 Combine like terms: -2.370928463 + -0.0769230769 = -2.4478515399 x = -2.4478515399 Simplifying x = -2.4478515399Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2940053861, -2.4478515399}
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