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Simplifying 26x(2 + -1x) + (4x + -5) = 0 (2 * 26x + -1x * 26x) + (4x + -5) = 0 (52x + -26x2) + (4x + -5) = 0 Reorder the terms: 52x + -26x2 + (-5 + 4x) = 0 Remove parenthesis around (-5 + 4x) 52x + -26x2 + -5 + 4x = 0 Reorder the terms: -5 + 52x + 4x + -26x2 = 0 Combine like terms: 52x + 4x = 56x -5 + 56x + -26x2 = 0 Solving -5 + 56x + -26x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -26 the coefficient of the squared term: Divide each side by '-26'. 0.1923076923 + -2.153846154x + x2 = 0 Move the constant term to the right: Add '-0.1923076923' to each side of the equation. 0.1923076923 + -2.153846154x + -0.1923076923 + x2 = 0 + -0.1923076923 Reorder the terms: 0.1923076923 + -0.1923076923 + -2.153846154x + x2 = 0 + -0.1923076923 Combine like terms: 0.1923076923 + -0.1923076923 = 0.0000000000 0.0000000000 + -2.153846154x + x2 = 0 + -0.1923076923 -2.153846154x + x2 = 0 + -0.1923076923 Combine like terms: 0 + -0.1923076923 = -0.1923076923 -2.153846154x + x2 = -0.1923076923 The x term is -2.153846154x. Take half its coefficient (-1.076923077). Square it (1.159763314) and add it to both sides. Add '1.159763314' to each side of the equation. -2.153846154x + 1.159763314 + x2 = -0.1923076923 + 1.159763314 Reorder the terms: 1.159763314 + -2.153846154x + x2 = -0.1923076923 + 1.159763314 Combine like terms: -0.1923076923 + 1.159763314 = 0.9674556217 1.159763314 + -2.153846154x + x2 = 0.9674556217 Factor a perfect square on the left side: (x + -1.076923077)(x + -1.076923077) = 0.9674556217 Calculate the square root of the right side: 0.98359322 Break this problem into two subproblems by setting (x + -1.076923077) equal to 0.98359322 and -0.98359322.Subproblem 1
x + -1.076923077 = 0.98359322 Simplifying x + -1.076923077 = 0.98359322 Reorder the terms: -1.076923077 + x = 0.98359322 Solving -1.076923077 + x = 0.98359322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.076923077' to each side of the equation. -1.076923077 + 1.076923077 + x = 0.98359322 + 1.076923077 Combine like terms: -1.076923077 + 1.076923077 = 0.000000000 0.000000000 + x = 0.98359322 + 1.076923077 x = 0.98359322 + 1.076923077 Combine like terms: 0.98359322 + 1.076923077 = 2.060516297 x = 2.060516297 Simplifying x = 2.060516297Subproblem 2
x + -1.076923077 = -0.98359322 Simplifying x + -1.076923077 = -0.98359322 Reorder the terms: -1.076923077 + x = -0.98359322 Solving -1.076923077 + x = -0.98359322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.076923077' to each side of the equation. -1.076923077 + 1.076923077 + x = -0.98359322 + 1.076923077 Combine like terms: -1.076923077 + 1.076923077 = 0.000000000 0.000000000 + x = -0.98359322 + 1.076923077 x = -0.98359322 + 1.076923077 Combine like terms: -0.98359322 + 1.076923077 = 0.093329857 x = 0.093329857 Simplifying x = 0.093329857Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.060516297, 0.093329857}
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