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Simplifying 21.25x2 + -72x + 55 = 0 Reorder the terms: 55 + -72x + 21.25x2 = 0 Solving 55 + -72x + 21.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 21.25 the coefficient of the squared term: Divide each side by '21.25'. 2.588235294 + -3.388235294x + x2 = 0 Move the constant term to the right: Add '-2.588235294' to each side of the equation. 2.588235294 + -3.388235294x + -2.588235294 + x2 = 0 + -2.588235294 Reorder the terms: 2.588235294 + -2.588235294 + -3.388235294x + x2 = 0 + -2.588235294 Combine like terms: 2.588235294 + -2.588235294 = 0.000000000 0.000000000 + -3.388235294x + x2 = 0 + -2.588235294 -3.388235294x + x2 = 0 + -2.588235294 Combine like terms: 0 + -2.588235294 = -2.588235294 -3.388235294x + x2 = -2.588235294 The x term is -3.388235294x. Take half its coefficient (-1.694117647). Square it (2.870034602) and add it to both sides. Add '2.870034602' to each side of the equation. -3.388235294x + 2.870034602 + x2 = -2.588235294 + 2.870034602 Reorder the terms: 2.870034602 + -3.388235294x + x2 = -2.588235294 + 2.870034602 Combine like terms: -2.588235294 + 2.870034602 = 0.281799308 2.870034602 + -3.388235294x + x2 = 0.281799308 Factor a perfect square on the left side: (x + -1.694117647)(x + -1.694117647) = 0.281799308 Calculate the square root of the right side: 0.530847726 Break this problem into two subproblems by setting (x + -1.694117647) equal to 0.530847726 and -0.530847726.Subproblem 1
x + -1.694117647 = 0.530847726 Simplifying x + -1.694117647 = 0.530847726 Reorder the terms: -1.694117647 + x = 0.530847726 Solving -1.694117647 + x = 0.530847726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.694117647' to each side of the equation. -1.694117647 + 1.694117647 + x = 0.530847726 + 1.694117647 Combine like terms: -1.694117647 + 1.694117647 = 0.000000000 0.000000000 + x = 0.530847726 + 1.694117647 x = 0.530847726 + 1.694117647 Combine like terms: 0.530847726 + 1.694117647 = 2.224965373 x = 2.224965373 Simplifying x = 2.224965373Subproblem 2
x + -1.694117647 = -0.530847726 Simplifying x + -1.694117647 = -0.530847726 Reorder the terms: -1.694117647 + x = -0.530847726 Solving -1.694117647 + x = -0.530847726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.694117647' to each side of the equation. -1.694117647 + 1.694117647 + x = -0.530847726 + 1.694117647 Combine like terms: -1.694117647 + 1.694117647 = 0.000000000 0.000000000 + x = -0.530847726 + 1.694117647 x = -0.530847726 + 1.694117647 Combine like terms: -0.530847726 + 1.694117647 = 1.163269921 x = 1.163269921 Simplifying x = 1.163269921Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.224965373, 1.163269921}
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