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Simplifying 2x2 + 36x + -576 = 0 Reorder the terms: -576 + 36x + 2x2 = 0 Solving -576 + 36x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-288 + 18x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-288 + 18x + x2)' equal to zero and attempt to solve: Simplifying -288 + 18x + x2 = 0 Solving -288 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '288' to each side of the equation. -288 + 18x + 288 + x2 = 0 + 288 Reorder the terms: -288 + 288 + 18x + x2 = 0 + 288 Combine like terms: -288 + 288 = 0 0 + 18x + x2 = 0 + 288 18x + x2 = 0 + 288 Combine like terms: 0 + 288 = 288 18x + x2 = 288 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = 288 + 81 Reorder the terms: 81 + 18x + x2 = 288 + 81 Combine like terms: 288 + 81 = 369 81 + 18x + x2 = 369 Factor a perfect square on the left side: (x + 9)(x + 9) = 369 Calculate the square root of the right side: 19.209372712 Break this problem into two subproblems by setting (x + 9) equal to 19.209372712 and -19.209372712.Subproblem 1
x + 9 = 19.209372712 Simplifying x + 9 = 19.209372712 Reorder the terms: 9 + x = 19.209372712 Solving 9 + x = 19.209372712 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 19.209372712 + -9 Combine like terms: 9 + -9 = 0 0 + x = 19.209372712 + -9 x = 19.209372712 + -9 Combine like terms: 19.209372712 + -9 = 10.209372712 x = 10.209372712 Simplifying x = 10.209372712Subproblem 2
x + 9 = -19.209372712 Simplifying x + 9 = -19.209372712 Reorder the terms: 9 + x = -19.209372712 Solving 9 + x = -19.209372712 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -19.209372712 + -9 Combine like terms: 9 + -9 = 0 0 + x = -19.209372712 + -9 x = -19.209372712 + -9 Combine like terms: -19.209372712 + -9 = -28.209372712 x = -28.209372712 Simplifying x = -28.209372712Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.209372712, -28.209372712}Solution
x = {10.209372712, -28.209372712}
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