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Simplifying (7x2 + -2x + 24) + (2x2 + 8x + -73) = 0 Reorder the terms: (24 + -2x + 7x2) + (2x2 + 8x + -73) = 0 Remove parenthesis around (24 + -2x + 7x2) 24 + -2x + 7x2 + (2x2 + 8x + -73) = 0 Reorder the terms: 24 + -2x + 7x2 + (-73 + 8x + 2x2) = 0 Remove parenthesis around (-73 + 8x + 2x2) 24 + -2x + 7x2 + -73 + 8x + 2x2 = 0 Reorder the terms: 24 + -73 + -2x + 8x + 7x2 + 2x2 = 0 Combine like terms: 24 + -73 = -49 -49 + -2x + 8x + 7x2 + 2x2 = 0 Combine like terms: -2x + 8x = 6x -49 + 6x + 7x2 + 2x2 = 0 Combine like terms: 7x2 + 2x2 = 9x2 -49 + 6x + 9x2 = 0 Solving -49 + 6x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -5.444444444 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '5.444444444' to each side of the equation. -5.444444444 + 0.6666666667x + 5.444444444 + x2 = 0 + 5.444444444 Reorder the terms: -5.444444444 + 5.444444444 + 0.6666666667x + x2 = 0 + 5.444444444 Combine like terms: -5.444444444 + 5.444444444 = 0.000000000 0.000000000 + 0.6666666667x + x2 = 0 + 5.444444444 0.6666666667x + x2 = 0 + 5.444444444 Combine like terms: 0 + 5.444444444 = 5.444444444 0.6666666667x + x2 = 5.444444444 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 5.444444444 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 5.444444444 + 0.1111111112 Combine like terms: 5.444444444 + 0.1111111112 = 5.5555555552 0.1111111112 + 0.6666666667x + x2 = 5.5555555552 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 5.5555555552 Calculate the square root of the right side: 2.357022604 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 2.357022604 and -2.357022604.Subproblem 1
x + 0.3333333334 = 2.357022604 Simplifying x + 0.3333333334 = 2.357022604 Reorder the terms: 0.3333333334 + x = 2.357022604 Solving 0.3333333334 + x = 2.357022604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 2.357022604 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 2.357022604 + -0.3333333334 x = 2.357022604 + -0.3333333334 Combine like terms: 2.357022604 + -0.3333333334 = 2.0236892706 x = 2.0236892706 Simplifying x = 2.0236892706Subproblem 2
x + 0.3333333334 = -2.357022604 Simplifying x + 0.3333333334 = -2.357022604 Reorder the terms: 0.3333333334 + x = -2.357022604 Solving 0.3333333334 + x = -2.357022604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -2.357022604 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -2.357022604 + -0.3333333334 x = -2.357022604 + -0.3333333334 Combine like terms: -2.357022604 + -0.3333333334 = -2.6903559374 x = -2.6903559374 Simplifying x = -2.6903559374Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.0236892706, -2.6903559374}
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