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Simplifying 26x2 + -100x + -96 = 0 Reorder the terms: -96 + -100x + 26x2 = 0 Solving -96 + -100x + 26x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-48 + -50x + 13x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-48 + -50x + 13x2)' equal to zero and attempt to solve: Simplifying -48 + -50x + 13x2 = 0 Solving -48 + -50x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -3.692307692 + -3.846153846x + x2 = 0 Move the constant term to the right: Add '3.692307692' to each side of the equation. -3.692307692 + -3.846153846x + 3.692307692 + x2 = 0 + 3.692307692 Reorder the terms: -3.692307692 + 3.692307692 + -3.846153846x + x2 = 0 + 3.692307692 Combine like terms: -3.692307692 + 3.692307692 = 0.000000000 0.000000000 + -3.846153846x + x2 = 0 + 3.692307692 -3.846153846x + x2 = 0 + 3.692307692 Combine like terms: 0 + 3.692307692 = 3.692307692 -3.846153846x + x2 = 3.692307692 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 = 3.692307692 + 3.698224852 Reorder the terms: 3.698224852 + -3.846153846x + x2 = 3.692307692 + 3.698224852 Combine like terms: 3.692307692 + 3.698224852 = 7.390532544 3.698224852 + -3.846153846x + x2 = 7.390532544 Factor a perfect square on the left side: (x + -1.923076923)(x + -1.923076923) = 7.390532544 Calculate the square root of the right side: 2.718553392 Break this problem into two subproblems by setting (x + -1.923076923) equal to 2.718553392 and -2.718553392.Subproblem 1
x + -1.923076923 = 2.718553392 Simplifying x + -1.923076923 = 2.718553392 Reorder the terms: -1.923076923 + x = 2.718553392 Solving -1.923076923 + x = 2.718553392 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 = 2.718553392 + 1.923076923 Combine like terms: -1.923076923 + 1.923076923 = 0.000000000 0.000000000 + x = 2.718553392 + 1.923076923 x = 2.718553392 + 1.923076923 Combine like terms: 2.718553392 + 1.923076923 = 4.641630315 x = 4.641630315 Simplifying x = 4.641630315Subproblem 2
x + -1.923076923 = -2.718553392 Simplifying x + -1.923076923 = -2.718553392 Reorder the terms: -1.923076923 + x = -2.718553392 Solving -1.923076923 + x = -2.718553392 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 = -2.718553392 + 1.923076923 Combine like terms: -1.923076923 + 1.923076923 = 0.000000000 0.000000000 + x = -2.718553392 + 1.923076923 x = -2.718553392 + 1.923076923 Combine like terms: -2.718553392 + 1.923076923 = -0.795476469 x = -0.795476469 Simplifying x = -0.795476469Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.641630315, -0.795476469}Solution
x = {4.641630315, -0.795476469}
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