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Simplifying x2 + 26x = 80 Reorder the terms: 26x + x2 = 80 Solving 26x + x2 = 80 Solving for variable 'x'. Reorder the terms: -80 + 26x + x2 = 80 + -80 Combine like terms: 80 + -80 = 0 -80 + 26x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '80' to each side of the equation. -80 + 26x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + 26x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + 26x + x2 = 0 + 80 26x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 26x + x2 = 80 The x term is 26x. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26x + 169 + x2 = 80 + 169 Reorder the terms: 169 + 26x + x2 = 80 + 169 Combine like terms: 80 + 169 = 249 169 + 26x + x2 = 249 Factor a perfect square on the left side: (x + 13)(x + 13) = 249 Calculate the square root of the right side: 15.779733838 Break this problem into two subproblems by setting (x + 13) equal to 15.779733838 and -15.779733838.Subproblem 1
x + 13 = 15.779733838 Simplifying x + 13 = 15.779733838 Reorder the terms: 13 + x = 15.779733838 Solving 13 + x = 15.779733838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = 15.779733838 + -13 Combine like terms: 13 + -13 = 0 0 + x = 15.779733838 + -13 x = 15.779733838 + -13 Combine like terms: 15.779733838 + -13 = 2.779733838 x = 2.779733838 Simplifying x = 2.779733838Subproblem 2
x + 13 = -15.779733838 Simplifying x + 13 = -15.779733838 Reorder the terms: 13 + x = -15.779733838 Solving 13 + x = -15.779733838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = -15.779733838 + -13 Combine like terms: 13 + -13 = 0 0 + x = -15.779733838 + -13 x = -15.779733838 + -13 Combine like terms: -15.779733838 + -13 = -28.779733838 x = -28.779733838 Simplifying x = -28.779733838Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.779733838, -28.779733838}
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