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Simplifying (7x2 + -4x + -5) + (6x2 + -1x + 2) = 0 Reorder the terms: (-5 + -4x + 7x2) + (6x2 + -1x + 2) = 0 Remove parenthesis around (-5 + -4x + 7x2) -5 + -4x + 7x2 + (6x2 + -1x + 2) = 0 Reorder the terms: -5 + -4x + 7x2 + (2 + -1x + 6x2) = 0 Remove parenthesis around (2 + -1x + 6x2) -5 + -4x + 7x2 + 2 + -1x + 6x2 = 0 Reorder the terms: -5 + 2 + -4x + -1x + 7x2 + 6x2 = 0 Combine like terms: -5 + 2 = -3 -3 + -4x + -1x + 7x2 + 6x2 = 0 Combine like terms: -4x + -1x = -5x -3 + -5x + 7x2 + 6x2 = 0 Combine like terms: 7x2 + 6x2 = 13x2 -3 + -5x + 13x2 = 0 Solving -3 + -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'. -0.2307692308 + -0.3846153846x + x2 = 0 Move the constant term to the right: Add '0.2307692308' to each side of the equation. -0.2307692308 + -0.3846153846x + 0.2307692308 + x2 = 0 + 0.2307692308 Reorder the terms: -0.2307692308 + 0.2307692308 + -0.3846153846x + x2 = 0 + 0.2307692308 Combine like terms: -0.2307692308 + 0.2307692308 = 0.0000000000 0.0000000000 + -0.3846153846x + x2 = 0 + 0.2307692308 -0.3846153846x + x2 = 0 + 0.2307692308 Combine like terms: 0 + 0.2307692308 = 0.2307692308 -0.3846153846x + x2 = 0.2307692308 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 = 0.2307692308 + 0.03698224852 Reorder the terms: 0.03698224852 + -0.3846153846x + x2 = 0.2307692308 + 0.03698224852 Combine like terms: 0.2307692308 + 0.03698224852 = 0.26775147932 0.03698224852 + -0.3846153846x + x2 = 0.26775147932 Factor a perfect square on the left side: (x + -0.1923076923)(x + -0.1923076923) = 0.26775147932 Calculate the square root of the right side: 0.517447079 Break this problem into two subproblems by setting (x + -0.1923076923) equal to 0.517447079 and -0.517447079.Subproblem 1
x + -0.1923076923 = 0.517447079 Simplifying x + -0.1923076923 = 0.517447079 Reorder the terms: -0.1923076923 + x = 0.517447079 Solving -0.1923076923 + x = 0.517447079 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 = 0.517447079 + 0.1923076923 Combine like terms: -0.1923076923 + 0.1923076923 = 0.0000000000 0.0000000000 + x = 0.517447079 + 0.1923076923 x = 0.517447079 + 0.1923076923 Combine like terms: 0.517447079 + 0.1923076923 = 0.7097547713 x = 0.7097547713 Simplifying x = 0.7097547713Subproblem 2
x + -0.1923076923 = -0.517447079 Simplifying x + -0.1923076923 = -0.517447079 Reorder the terms: -0.1923076923 + x = -0.517447079 Solving -0.1923076923 + x = -0.517447079 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 = -0.517447079 + 0.1923076923 Combine like terms: -0.1923076923 + 0.1923076923 = 0.0000000000 0.0000000000 + x = -0.517447079 + 0.1923076923 x = -0.517447079 + 0.1923076923 Combine like terms: -0.517447079 + 0.1923076923 = -0.3251393867 x = -0.3251393867 Simplifying x = -0.3251393867Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7097547713, -0.3251393867}
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