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Simplifying x2 + 6x + -240 = 0 Reorder the terms: -240 + 6x + x2 = 0 Solving -240 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '240' to each side of the equation. -240 + 6x + 240 + x2 = 0 + 240 Reorder the terms: -240 + 240 + 6x + x2 = 0 + 240 Combine like terms: -240 + 240 = 0 0 + 6x + x2 = 0 + 240 6x + x2 = 0 + 240 Combine like terms: 0 + 240 = 240 6x + x2 = 240 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 240 + 9 Reorder the terms: 9 + 6x + x2 = 240 + 9 Combine like terms: 240 + 9 = 249 9 + 6x + x2 = 249 Factor a perfect square on the left side: (x + 3)(x + 3) = 249 Calculate the square root of the right side: 15.779733838 Break this problem into two subproblems by setting (x + 3) equal to 15.779733838 and -15.779733838.Subproblem 1
x + 3 = 15.779733838 Simplifying x + 3 = 15.779733838 Reorder the terms: 3 + x = 15.779733838 Solving 3 + x = 15.779733838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 15.779733838 + -3 Combine like terms: 3 + -3 = 0 0 + x = 15.779733838 + -3 x = 15.779733838 + -3 Combine like terms: 15.779733838 + -3 = 12.779733838 x = 12.779733838 Simplifying x = 12.779733838Subproblem 2
x + 3 = -15.779733838 Simplifying x + 3 = -15.779733838 Reorder the terms: 3 + x = -15.779733838 Solving 3 + x = -15.779733838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -15.779733838 + -3 Combine like terms: 3 + -3 = 0 0 + x = -15.779733838 + -3 x = -15.779733838 + -3 Combine like terms: -15.779733838 + -3 = -18.779733838 x = -18.779733838 Simplifying x = -18.779733838Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.779733838, -18.779733838}
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