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Simplifying 13x2 + 5x + -5 = 0 Reorder the terms: -5 + 5x + 13x2 = 0 Solving -5 + 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'. -0.3846153846 + 0.3846153846x + x2 = 0 Move the constant term to the right: Add '0.3846153846' to each side of the equation. -0.3846153846 + 0.3846153846x + 0.3846153846 + x2 = 0 + 0.3846153846 Reorder the terms: -0.3846153846 + 0.3846153846 + 0.3846153846x + x2 = 0 + 0.3846153846 Combine like terms: -0.3846153846 + 0.3846153846 = 0.0000000000 0.0000000000 + 0.3846153846x + x2 = 0 + 0.3846153846 0.3846153846x + x2 = 0 + 0.3846153846 Combine like terms: 0 + 0.3846153846 = 0.3846153846 0.3846153846x + x2 = 0.3846153846 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 = 0.3846153846 + 0.03698224852 Reorder the terms: 0.03698224852 + 0.3846153846x + x2 = 0.3846153846 + 0.03698224852 Combine like terms: 0.3846153846 + 0.03698224852 = 0.42159763312 0.03698224852 + 0.3846153846x + x2 = 0.42159763312 Factor a perfect square on the left side: (x + 0.1923076923)(x + 0.1923076923) = 0.42159763312 Calculate the square root of the right side: 0.649305501 Break this problem into two subproblems by setting (x + 0.1923076923) equal to 0.649305501 and -0.649305501.Subproblem 1
x + 0.1923076923 = 0.649305501 Simplifying x + 0.1923076923 = 0.649305501 Reorder the terms: 0.1923076923 + x = 0.649305501 Solving 0.1923076923 + x = 0.649305501 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 = 0.649305501 + -0.1923076923 Combine like terms: 0.1923076923 + -0.1923076923 = 0.0000000000 0.0000000000 + x = 0.649305501 + -0.1923076923 x = 0.649305501 + -0.1923076923 Combine like terms: 0.649305501 + -0.1923076923 = 0.4569978087 x = 0.4569978087 Simplifying x = 0.4569978087Subproblem 2
x + 0.1923076923 = -0.649305501 Simplifying x + 0.1923076923 = -0.649305501 Reorder the terms: 0.1923076923 + x = -0.649305501 Solving 0.1923076923 + x = -0.649305501 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 = -0.649305501 + -0.1923076923 Combine like terms: 0.1923076923 + -0.1923076923 = 0.0000000000 0.0000000000 + x = -0.649305501 + -0.1923076923 x = -0.649305501 + -0.1923076923 Combine like terms: -0.649305501 + -0.1923076923 = -0.8416131933 x = -0.8416131933 Simplifying x = -0.8416131933Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4569978087, -0.8416131933}
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