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Simplifying 2(13x2 + 35x + -52) = 0 Reorder the terms: 2(-52 + 35x + 13x2) = 0 (-52 * 2 + 35x * 2 + 13x2 * 2) = 0 (-104 + 70x + 26x2) = 0 Solving -104 + 70x + 26x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-52 + 35x + 13x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-52 + 35x + 13x2)' equal to zero and attempt to solve: Simplifying -52 + 35x + 13x2 = 0 Solving -52 + 35x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -4 + 2.692307692x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 2.692307692x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 2.692307692x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 2.692307692x + x2 = 0 + 4 2.692307692x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 2.692307692x + x2 = 4 The x term is 2.692307692x. Take half its coefficient (1.346153846). Square it (1.812130177) and add it to both sides. Add '1.812130177' to each side of the equation. 2.692307692x + 1.812130177 + x2 = 4 + 1.812130177 Reorder the terms: 1.812130177 + 2.692307692x + x2 = 4 + 1.812130177 Combine like terms: 4 + 1.812130177 = 5.812130177 1.812130177 + 2.692307692x + x2 = 5.812130177 Factor a perfect square on the left side: (x + 1.346153846)(x + 1.346153846) = 5.812130177 Calculate the square root of the right side: 2.410835991 Break this problem into two subproblems by setting (x + 1.346153846) equal to 2.410835991 and -2.410835991.Subproblem 1
x + 1.346153846 = 2.410835991 Simplifying x + 1.346153846 = 2.410835991 Reorder the terms: 1.346153846 + x = 2.410835991 Solving 1.346153846 + x = 2.410835991 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.346153846' to each side of the equation. 1.346153846 + -1.346153846 + x = 2.410835991 + -1.346153846 Combine like terms: 1.346153846 + -1.346153846 = 0.000000000 0.000000000 + x = 2.410835991 + -1.346153846 x = 2.410835991 + -1.346153846 Combine like terms: 2.410835991 + -1.346153846 = 1.064682145 x = 1.064682145 Simplifying x = 1.064682145Subproblem 2
x + 1.346153846 = -2.410835991 Simplifying x + 1.346153846 = -2.410835991 Reorder the terms: 1.346153846 + x = -2.410835991 Solving 1.346153846 + x = -2.410835991 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.346153846' to each side of the equation. 1.346153846 + -1.346153846 + x = -2.410835991 + -1.346153846 Combine like terms: 1.346153846 + -1.346153846 = 0.000000000 0.000000000 + x = -2.410835991 + -1.346153846 x = -2.410835991 + -1.346153846 Combine like terms: -2.410835991 + -1.346153846 = -3.756989837 x = -3.756989837 Simplifying x = -3.756989837Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.064682145, -3.756989837}Solution
x = {1.064682145, -3.756989837}
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