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Simplifying 20x + x2 = 1260 Solving 20x + x2 = 1260 Solving for variable 'x'. Reorder the terms: -1260 + 20x + x2 = 1260 + -1260 Combine like terms: 1260 + -1260 = 0 -1260 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1260' to each side of the equation. -1260 + 20x + 1260 + x2 = 0 + 1260 Reorder the terms: -1260 + 1260 + 20x + x2 = 0 + 1260 Combine like terms: -1260 + 1260 = 0 0 + 20x + x2 = 0 + 1260 20x + x2 = 0 + 1260 Combine like terms: 0 + 1260 = 1260 20x + x2 = 1260 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 = 1260 + 100 Reorder the terms: 100 + 20x + x2 = 1260 + 100 Combine like terms: 1260 + 100 = 1360 100 + 20x + x2 = 1360 Factor a perfect square on the left side: (x + 10)(x + 10) = 1360 Calculate the square root of the right side: 36.878177829 Break this problem into two subproblems by setting (x + 10) equal to 36.878177829 and -36.878177829.Subproblem 1
x + 10 = 36.878177829 Simplifying x + 10 = 36.878177829 Reorder the terms: 10 + x = 36.878177829 Solving 10 + x = 36.878177829 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 = 36.878177829 + -10 Combine like terms: 10 + -10 = 0 0 + x = 36.878177829 + -10 x = 36.878177829 + -10 Combine like terms: 36.878177829 + -10 = 26.878177829 x = 26.878177829 Simplifying x = 26.878177829Subproblem 2
x + 10 = -36.878177829 Simplifying x + 10 = -36.878177829 Reorder the terms: 10 + x = -36.878177829 Solving 10 + x = -36.878177829 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 = -36.878177829 + -10 Combine like terms: 10 + -10 = 0 0 + x = -36.878177829 + -10 x = -36.878177829 + -10 Combine like terms: -36.878177829 + -10 = -46.878177829 x = -46.878177829 Simplifying x = -46.878177829Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.878177829, -46.878177829}
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