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Simplifying (7x2 + -2x + 13) + (6x2 + 9x + -72) = 0 Reorder the terms: (13 + -2x + 7x2) + (6x2 + 9x + -72) = 0 Remove parenthesis around (13 + -2x + 7x2) 13 + -2x + 7x2 + (6x2 + 9x + -72) = 0 Reorder the terms: 13 + -2x + 7x2 + (-72 + 9x + 6x2) = 0 Remove parenthesis around (-72 + 9x + 6x2) 13 + -2x + 7x2 + -72 + 9x + 6x2 = 0 Reorder the terms: 13 + -72 + -2x + 9x + 7x2 + 6x2 = 0 Combine like terms: 13 + -72 = -59 -59 + -2x + 9x + 7x2 + 6x2 = 0 Combine like terms: -2x + 9x = 7x -59 + 7x + 7x2 + 6x2 = 0 Combine like terms: 7x2 + 6x2 = 13x2 -59 + 7x + 13x2 = 0 Solving -59 + 7x + 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'. -4.538461538 + 0.5384615385x + x2 = 0 Move the constant term to the right: Add '4.538461538' to each side of the equation. -4.538461538 + 0.5384615385x + 4.538461538 + x2 = 0 + 4.538461538 Reorder the terms: -4.538461538 + 4.538461538 + 0.5384615385x + x2 = 0 + 4.538461538 Combine like terms: -4.538461538 + 4.538461538 = 0.000000000 0.000000000 + 0.5384615385x + x2 = 0 + 4.538461538 0.5384615385x + x2 = 0 + 4.538461538 Combine like terms: 0 + 4.538461538 = 4.538461538 0.5384615385x + x2 = 4.538461538 The x term is 0.5384615385x. Take half its coefficient (0.2692307693). Square it (0.07248520714) and add it to both sides. Add '0.07248520714' to each side of the equation. 0.5384615385x + 0.07248520714 + x2 = 4.538461538 + 0.07248520714 Reorder the terms: 0.07248520714 + 0.5384615385x + x2 = 4.538461538 + 0.07248520714 Combine like terms: 4.538461538 + 0.07248520714 = 4.61094674514 0.07248520714 + 0.5384615385x + x2 = 4.61094674514 Factor a perfect square on the left side: (x + 0.2692307693)(x + 0.2692307693) = 4.61094674514 Calculate the square root of the right side: 2.147311516 Break this problem into two subproblems by setting (x + 0.2692307693) equal to 2.147311516 and -2.147311516.Subproblem 1
x + 0.2692307693 = 2.147311516 Simplifying x + 0.2692307693 = 2.147311516 Reorder the terms: 0.2692307693 + x = 2.147311516 Solving 0.2692307693 + x = 2.147311516 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2692307693' to each side of the equation. 0.2692307693 + -0.2692307693 + x = 2.147311516 + -0.2692307693 Combine like terms: 0.2692307693 + -0.2692307693 = 0.0000000000 0.0000000000 + x = 2.147311516 + -0.2692307693 x = 2.147311516 + -0.2692307693 Combine like terms: 2.147311516 + -0.2692307693 = 1.8780807467 x = 1.8780807467 Simplifying x = 1.8780807467Subproblem 2
x + 0.2692307693 = -2.147311516 Simplifying x + 0.2692307693 = -2.147311516 Reorder the terms: 0.2692307693 + x = -2.147311516 Solving 0.2692307693 + x = -2.147311516 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2692307693' to each side of the equation. 0.2692307693 + -0.2692307693 + x = -2.147311516 + -0.2692307693 Combine like terms: 0.2692307693 + -0.2692307693 = 0.0000000000 0.0000000000 + x = -2.147311516 + -0.2692307693 x = -2.147311516 + -0.2692307693 Combine like terms: -2.147311516 + -0.2692307693 = -2.4165422853 x = -2.4165422853 Simplifying x = -2.4165422853Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8780807467, -2.4165422853}
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