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Simplifying 13x2 + 50x + 39 = 0 Reorder the terms: 39 + 50x + 13x2 = 0 Solving 39 + 50x + 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 + 3.846153846x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 3.846153846x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 3.846153846x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 3.846153846x + x2 = 0 + -3 3.846153846x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 3.846153846x + x2 = -3 The x term is 3.846153846x. Take half its coefficient (1.923076923). Square it (3.698224852) and add it to both sides. Add '3.698224852' to each side of the equation. 3.846153846x + 3.698224852 + x2 = -3 + 3.698224852 Reorder the terms: 3.698224852 + 3.846153846x + x2 = -3 + 3.698224852 Combine like terms: -3 + 3.698224852 = 0.698224852 3.698224852 + 3.846153846x + x2 = 0.698224852 Factor a perfect square on the left side: (x + 1.923076923)(x + 1.923076923) = 0.698224852 Calculate the square root of the right side: 0.835598499 Break this problem into two subproblems by setting (x + 1.923076923) equal to 0.835598499 and -0.835598499.Subproblem 1
x + 1.923076923 = 0.835598499 Simplifying x + 1.923076923 = 0.835598499 Reorder the terms: 1.923076923 + x = 0.835598499 Solving 1.923076923 + x = 0.835598499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.923076923' to each side of the equation. 1.923076923 + -1.923076923 + x = 0.835598499 + -1.923076923 Combine like terms: 1.923076923 + -1.923076923 = 0.000000000 0.000000000 + x = 0.835598499 + -1.923076923 x = 0.835598499 + -1.923076923 Combine like terms: 0.835598499 + -1.923076923 = -1.087478424 x = -1.087478424 Simplifying x = -1.087478424Subproblem 2
x + 1.923076923 = -0.835598499 Simplifying x + 1.923076923 = -0.835598499 Reorder the terms: 1.923076923 + x = -0.835598499 Solving 1.923076923 + x = -0.835598499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.923076923' to each side of the equation. 1.923076923 + -1.923076923 + x = -0.835598499 + -1.923076923 Combine like terms: 1.923076923 + -1.923076923 = 0.000000000 0.000000000 + x = -0.835598499 + -1.923076923 x = -0.835598499 + -1.923076923 Combine like terms: -0.835598499 + -1.923076923 = -2.758675422 x = -2.758675422 Simplifying x = -2.758675422Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.087478424, -2.758675422}
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