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Simplifying x2 + -20x + 26.04 = 0 Reorder the terms: 26.04 + -20x + x2 = 0 Solving 26.04 + -20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-26.04' to each side of the equation. 26.04 + -20x + -26.04 + x2 = 0 + -26.04 Reorder the terms: 26.04 + -26.04 + -20x + x2 = 0 + -26.04 Combine like terms: 26.04 + -26.04 = 0.00 0.00 + -20x + x2 = 0 + -26.04 -20x + x2 = 0 + -26.04 Combine like terms: 0 + -26.04 = -26.04 -20x + x2 = -26.04 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -26.04 + 100 Reorder the terms: 100 + -20x + x2 = -26.04 + 100 Combine like terms: -26.04 + 100 = 73.96 100 + -20x + x2 = 73.96 Factor a perfect square on the left side: (x + -10)(x + -10) = 73.96 Calculate the square root of the right side: 8.6 Break this problem into two subproblems by setting (x + -10) equal to 8.6 and -8.6.Subproblem 1
x + -10 = 8.6 Simplifying x + -10 = 8.6 Reorder the terms: -10 + x = 8.6 Solving -10 + x = 8.6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 8.6 + 10 Combine like terms: -10 + 10 = 0 0 + x = 8.6 + 10 x = 8.6 + 10 Combine like terms: 8.6 + 10 = 18.6 x = 18.6 Simplifying x = 18.6Subproblem 2
x + -10 = -8.6 Simplifying x + -10 = -8.6 Reorder the terms: -10 + x = -8.6 Solving -10 + x = -8.6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -8.6 + 10 Combine like terms: -10 + 10 = 0 0 + x = -8.6 + 10 x = -8.6 + 10 Combine like terms: -8.6 + 10 = 1.4 x = 1.4 Simplifying x = 1.4Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.6, 1.4}
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