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Simplifying 13x2 + -5x + -4 = 0 Reorder the terms: -4 + -5x + 13x2 = 0 Solving -4 + -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'. -0.3076923077 + -0.3846153846x + x2 = 0 Move the constant term to the right: Add '0.3076923077' to each side of the equation. -0.3076923077 + -0.3846153846x + 0.3076923077 + x2 = 0 + 0.3076923077 Reorder the terms: -0.3076923077 + 0.3076923077 + -0.3846153846x + x2 = 0 + 0.3076923077 Combine like terms: -0.3076923077 + 0.3076923077 = 0.0000000000 0.0000000000 + -0.3846153846x + x2 = 0 + 0.3076923077 -0.3846153846x + x2 = 0 + 0.3076923077 Combine like terms: 0 + 0.3076923077 = 0.3076923077 -0.3846153846x + x2 = 0.3076923077 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 = 0.3076923077 + 0.03698224852 Reorder the terms: 0.03698224852 + -0.3846153846x + x2 = 0.3076923077 + 0.03698224852 Combine like terms: 0.3076923077 + 0.03698224852 = 0.34467455622 0.03698224852 + -0.3846153846x + x2 = 0.34467455622 Factor a perfect square on the left side: (x + -0.1923076923)(x + -0.1923076923) = 0.34467455622 Calculate the square root of the right side: 0.587089905 Break this problem into two subproblems by setting (x + -0.1923076923) equal to 0.587089905 and -0.587089905.Subproblem 1
x + -0.1923076923 = 0.587089905 Simplifying x + -0.1923076923 = 0.587089905 Reorder the terms: -0.1923076923 + x = 0.587089905 Solving -0.1923076923 + x = 0.587089905 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 = 0.587089905 + 0.1923076923 Combine like terms: -0.1923076923 + 0.1923076923 = 0.0000000000 0.0000000000 + x = 0.587089905 + 0.1923076923 x = 0.587089905 + 0.1923076923 Combine like terms: 0.587089905 + 0.1923076923 = 0.7793975973 x = 0.7793975973 Simplifying x = 0.7793975973Subproblem 2
x + -0.1923076923 = -0.587089905 Simplifying x + -0.1923076923 = -0.587089905 Reorder the terms: -0.1923076923 + x = -0.587089905 Solving -0.1923076923 + x = -0.587089905 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 = -0.587089905 + 0.1923076923 Combine like terms: -0.1923076923 + 0.1923076923 = 0.0000000000 0.0000000000 + x = -0.587089905 + 0.1923076923 x = -0.587089905 + 0.1923076923 Combine like terms: -0.587089905 + 0.1923076923 = -0.3947822127 x = -0.3947822127 Simplifying x = -0.3947822127Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7793975973, -0.3947822127}
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