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Simplifying (9x2 + -3x + 25) + (2x2 + 6x + -48) = 0 Reorder the terms: (25 + -3x + 9x2) + (2x2 + 6x + -48) = 0 Remove parenthesis around (25 + -3x + 9x2) 25 + -3x + 9x2 + (2x2 + 6x + -48) = 0 Reorder the terms: 25 + -3x + 9x2 + (-48 + 6x + 2x2) = 0 Remove parenthesis around (-48 + 6x + 2x2) 25 + -3x + 9x2 + -48 + 6x + 2x2 = 0 Reorder the terms: 25 + -48 + -3x + 6x + 9x2 + 2x2 = 0 Combine like terms: 25 + -48 = -23 -23 + -3x + 6x + 9x2 + 2x2 = 0 Combine like terms: -3x + 6x = 3x -23 + 3x + 9x2 + 2x2 = 0 Combine like terms: 9x2 + 2x2 = 11x2 -23 + 3x + 11x2 = 0 Solving -23 + 3x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -2.090909091 + 0.2727272727x + x2 = 0 Move the constant term to the right: Add '2.090909091' to each side of the equation. -2.090909091 + 0.2727272727x + 2.090909091 + x2 = 0 + 2.090909091 Reorder the terms: -2.090909091 + 2.090909091 + 0.2727272727x + x2 = 0 + 2.090909091 Combine like terms: -2.090909091 + 2.090909091 = 0.000000000 0.000000000 + 0.2727272727x + x2 = 0 + 2.090909091 0.2727272727x + x2 = 0 + 2.090909091 Combine like terms: 0 + 2.090909091 = 2.090909091 0.2727272727x + x2 = 2.090909091 The x term is 0.2727272727x. Take half its coefficient (0.1363636364). Square it (0.01859504133) and add it to both sides. Add '0.01859504133' to each side of the equation. 0.2727272727x + 0.01859504133 + x2 = 2.090909091 + 0.01859504133 Reorder the terms: 0.01859504133 + 0.2727272727x + x2 = 2.090909091 + 0.01859504133 Combine like terms: 2.090909091 + 0.01859504133 = 2.10950413233 0.01859504133 + 0.2727272727x + x2 = 2.10950413233 Factor a perfect square on the left side: (x + 0.1363636364)(x + 0.1363636364) = 2.10950413233 Calculate the square root of the right side: 1.45241321 Break this problem into two subproblems by setting (x + 0.1363636364) equal to 1.45241321 and -1.45241321.Subproblem 1
x + 0.1363636364 = 1.45241321 Simplifying x + 0.1363636364 = 1.45241321 Reorder the terms: 0.1363636364 + x = 1.45241321 Solving 0.1363636364 + x = 1.45241321 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1363636364' to each side of the equation. 0.1363636364 + -0.1363636364 + x = 1.45241321 + -0.1363636364 Combine like terms: 0.1363636364 + -0.1363636364 = 0.0000000000 0.0000000000 + x = 1.45241321 + -0.1363636364 x = 1.45241321 + -0.1363636364 Combine like terms: 1.45241321 + -0.1363636364 = 1.3160495736 x = 1.3160495736 Simplifying x = 1.3160495736Subproblem 2
x + 0.1363636364 = -1.45241321 Simplifying x + 0.1363636364 = -1.45241321 Reorder the terms: 0.1363636364 + x = -1.45241321 Solving 0.1363636364 + x = -1.45241321 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1363636364' to each side of the equation. 0.1363636364 + -0.1363636364 + x = -1.45241321 + -0.1363636364 Combine like terms: 0.1363636364 + -0.1363636364 = 0.0000000000 0.0000000000 + x = -1.45241321 + -0.1363636364 x = -1.45241321 + -0.1363636364 Combine like terms: -1.45241321 + -0.1363636364 = -1.5887768464 x = -1.5887768464 Simplifying x = -1.5887768464Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3160495736, -1.5887768464}
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