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Simplifying (7x2 + -2x + -45) + (6x2 + 7x) = 0 Reorder the terms: (-45 + -2x + 7x2) + (6x2 + 7x) = 0 Remove parenthesis around (-45 + -2x + 7x2) -45 + -2x + 7x2 + (6x2 + 7x) = 0 Reorder the terms: -45 + -2x + 7x2 + (7x + 6x2) = 0 Remove parenthesis around (7x + 6x2) -45 + -2x + 7x2 + 7x + 6x2 = 0 Reorder the terms: -45 + -2x + 7x + 7x2 + 6x2 = 0 Combine like terms: -2x + 7x = 5x -45 + 5x + 7x2 + 6x2 = 0 Combine like terms: 7x2 + 6x2 = 13x2 -45 + 5x + 13x2 = 0 Solving -45 + 5x + 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'. -3.461538462 + 0.3846153846x + x2 = 0 Move the constant term to the right: Add '3.461538462' to each side of the equation. -3.461538462 + 0.3846153846x + 3.461538462 + x2 = 0 + 3.461538462 Reorder the terms: -3.461538462 + 3.461538462 + 0.3846153846x + x2 = 0 + 3.461538462 Combine like terms: -3.461538462 + 3.461538462 = 0.000000000 0.000000000 + 0.3846153846x + x2 = 0 + 3.461538462 0.3846153846x + x2 = 0 + 3.461538462 Combine like terms: 0 + 3.461538462 = 3.461538462 0.3846153846x + x2 = 3.461538462 The x term is 0.3846153846x. Take half its coefficient (0.1923076923). Square it (0.03698224852) and add it to both sides. Add '0.03698224852' to each side of the equation. 0.3846153846x + 0.03698224852 + x2 = 3.461538462 + 0.03698224852 Reorder the terms: 0.03698224852 + 0.3846153846x + x2 = 3.461538462 + 0.03698224852 Combine like terms: 3.461538462 + 0.03698224852 = 3.49852071052 0.03698224852 + 0.3846153846x + x2 = 3.49852071052 Factor a perfect square on the left side: (x + 0.1923076923)(x + 0.1923076923) = 3.49852071052 Calculate the square root of the right side: 1.870433295 Break this problem into two subproblems by setting (x + 0.1923076923) equal to 1.870433295 and -1.870433295.Subproblem 1
x + 0.1923076923 = 1.870433295 Simplifying x + 0.1923076923 = 1.870433295 Reorder the terms: 0.1923076923 + x = 1.870433295 Solving 0.1923076923 + x = 1.870433295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1923076923' to each side of the equation. 0.1923076923 + -0.1923076923 + x = 1.870433295 + -0.1923076923 Combine like terms: 0.1923076923 + -0.1923076923 = 0.0000000000 0.0000000000 + x = 1.870433295 + -0.1923076923 x = 1.870433295 + -0.1923076923 Combine like terms: 1.870433295 + -0.1923076923 = 1.6781256027 x = 1.6781256027 Simplifying x = 1.6781256027Subproblem 2
x + 0.1923076923 = -1.870433295 Simplifying x + 0.1923076923 = -1.870433295 Reorder the terms: 0.1923076923 + x = -1.870433295 Solving 0.1923076923 + x = -1.870433295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1923076923' to each side of the equation. 0.1923076923 + -0.1923076923 + x = -1.870433295 + -0.1923076923 Combine like terms: 0.1923076923 + -0.1923076923 = 0.0000000000 0.0000000000 + x = -1.870433295 + -0.1923076923 x = -1.870433295 + -0.1923076923 Combine like terms: -1.870433295 + -0.1923076923 = -2.0627409873 x = -2.0627409873 Simplifying x = -2.0627409873Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6781256027, -2.0627409873}
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