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Simplifying 26x2 + -56x + 21 = 0 Reorder the terms: 21 + -56x + 26x2 = 0 Solving 21 + -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'. 0.8076923077 + -2.153846154x + x2 = 0 Move the constant term to the right: Add '-0.8076923077' to each side of the equation. 0.8076923077 + -2.153846154x + -0.8076923077 + x2 = 0 + -0.8076923077 Reorder the terms: 0.8076923077 + -0.8076923077 + -2.153846154x + x2 = 0 + -0.8076923077 Combine like terms: 0.8076923077 + -0.8076923077 = 0.0000000000 0.0000000000 + -2.153846154x + x2 = 0 + -0.8076923077 -2.153846154x + x2 = 0 + -0.8076923077 Combine like terms: 0 + -0.8076923077 = -0.8076923077 -2.153846154x + x2 = -0.8076923077 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 = -0.8076923077 + 1.159763314 Reorder the terms: 1.159763314 + -2.153846154x + x2 = -0.8076923077 + 1.159763314 Combine like terms: -0.8076923077 + 1.159763314 = 0.3520710063 1.159763314 + -2.153846154x + x2 = 0.3520710063 Factor a perfect square on the left side: (x + -1.076923077)(x + -1.076923077) = 0.3520710063 Calculate the square root of the right side: 0.593355716 Break this problem into two subproblems by setting (x + -1.076923077) equal to 0.593355716 and -0.593355716.Subproblem 1
x + -1.076923077 = 0.593355716 Simplifying x + -1.076923077 = 0.593355716 Reorder the terms: -1.076923077 + x = 0.593355716 Solving -1.076923077 + x = 0.593355716 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 = 0.593355716 + 1.076923077 Combine like terms: -1.076923077 + 1.076923077 = 0.000000000 0.000000000 + x = 0.593355716 + 1.076923077 x = 0.593355716 + 1.076923077 Combine like terms: 0.593355716 + 1.076923077 = 1.670278793 x = 1.670278793 Simplifying x = 1.670278793Subproblem 2
x + -1.076923077 = -0.593355716 Simplifying x + -1.076923077 = -0.593355716 Reorder the terms: -1.076923077 + x = -0.593355716 Solving -1.076923077 + x = -0.593355716 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 = -0.593355716 + 1.076923077 Combine like terms: -1.076923077 + 1.076923077 = 0.000000000 0.000000000 + x = -0.593355716 + 1.076923077 x = -0.593355716 + 1.076923077 Combine like terms: -0.593355716 + 1.076923077 = 0.483567361 x = 0.483567361 Simplifying x = 0.483567361Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.670278793, 0.483567361}
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