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Simplifying (6x2) + -1(5x + -6) + (7x2 + -7) = 0 Reorder the terms: (6x2) + -1(-6 + 5x) + (7x2 + -7) = 0 (6x2) + (-6 * -1 + 5x * -1) + (7x2 + -7) = 0 (6x2) + (6 + -5x) + (7x2 + -7) = 0 Reorder the terms: (6x2) + 6 + -5x + (-7 + 7x2) = 0 Remove parenthesis around (-7 + 7x2) (6x2) + 6 + -5x + -7 + 7x2 = 0 Reorder the terms: 6 + -7 + -5x + (6x2) + 7x2 = 0 Combine like terms: 6 + -7 = -1 -1 + -5x + (6x2) + 7x2 = 0 Combine like terms: (6x2) + 7x2 = 13x2 -1 + -5x + 13x2 = 0 Solving -1 + -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'. -0.07692307692 + -0.3846153846x + x2 = 0 Move the constant term to the right: Add '0.07692307692' to each side of the equation. -0.07692307692 + -0.3846153846x + 0.07692307692 + x2 = 0 + 0.07692307692 Reorder the terms: -0.07692307692 + 0.07692307692 + -0.3846153846x + x2 = 0 + 0.07692307692 Combine like terms: -0.07692307692 + 0.07692307692 = 0.00000000000 0.00000000000 + -0.3846153846x + x2 = 0 + 0.07692307692 -0.3846153846x + x2 = 0 + 0.07692307692 Combine like terms: 0 + 0.07692307692 = 0.07692307692 -0.3846153846x + x2 = 0.07692307692 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 = 0.07692307692 + 0.03698224852 Reorder the terms: 0.03698224852 + -0.3846153846x + x2 = 0.07692307692 + 0.03698224852 Combine like terms: 0.07692307692 + 0.03698224852 = 0.11390532544 0.03698224852 + -0.3846153846x + x2 = 0.11390532544 Factor a perfect square on the left side: (x + -0.1923076923)(x + -0.1923076923) = 0.11390532544 Calculate the square root of the right side: 0.33749863 Break this problem into two subproblems by setting (x + -0.1923076923) equal to 0.33749863 and -0.33749863.Subproblem 1
x + -0.1923076923 = 0.33749863 Simplifying x + -0.1923076923 = 0.33749863 Reorder the terms: -0.1923076923 + x = 0.33749863 Solving -0.1923076923 + x = 0.33749863 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 = 0.33749863 + 0.1923076923 Combine like terms: -0.1923076923 + 0.1923076923 = 0.0000000000 0.0000000000 + x = 0.33749863 + 0.1923076923 x = 0.33749863 + 0.1923076923 Combine like terms: 0.33749863 + 0.1923076923 = 0.5298063223 x = 0.5298063223 Simplifying x = 0.5298063223Subproblem 2
x + -0.1923076923 = -0.33749863 Simplifying x + -0.1923076923 = -0.33749863 Reorder the terms: -0.1923076923 + x = -0.33749863 Solving -0.1923076923 + x = -0.33749863 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 = -0.33749863 + 0.1923076923 Combine like terms: -0.1923076923 + 0.1923076923 = 0.0000000000 0.0000000000 + x = -0.33749863 + 0.1923076923 x = -0.33749863 + 0.1923076923 Combine like terms: -0.33749863 + 0.1923076923 = -0.1451909377 x = -0.1451909377 Simplifying x = -0.1451909377Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5298063223, -0.1451909377}
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