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Simplifying 2x2 + 36x + 56 = 0 Reorder the terms: 56 + 36x + 2x2 = 0 Solving 56 + 36x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(28 + 18x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(28 + 18x + x2)' equal to zero and attempt to solve: Simplifying 28 + 18x + x2 = 0 Solving 28 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-28' to each side of the equation. 28 + 18x + -28 + x2 = 0 + -28 Reorder the terms: 28 + -28 + 18x + x2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + 18x + x2 = 0 + -28 18x + x2 = 0 + -28 Combine like terms: 0 + -28 = -28 18x + x2 = -28 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 = -28 + 81 Reorder the terms: 81 + 18x + x2 = -28 + 81 Combine like terms: -28 + 81 = 53 81 + 18x + x2 = 53 Factor a perfect square on the left side: (x + 9)(x + 9) = 53 Calculate the square root of the right side: 7.280109889 Break this problem into two subproblems by setting (x + 9) equal to 7.280109889 and -7.280109889.Subproblem 1
x + 9 = 7.280109889 Simplifying x + 9 = 7.280109889 Reorder the terms: 9 + x = 7.280109889 Solving 9 + x = 7.280109889 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 = 7.280109889 + -9 Combine like terms: 9 + -9 = 0 0 + x = 7.280109889 + -9 x = 7.280109889 + -9 Combine like terms: 7.280109889 + -9 = -1.719890111 x = -1.719890111 Simplifying x = -1.719890111Subproblem 2
x + 9 = -7.280109889 Simplifying x + 9 = -7.280109889 Reorder the terms: 9 + x = -7.280109889 Solving 9 + x = -7.280109889 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 = -7.280109889 + -9 Combine like terms: 9 + -9 = 0 0 + x = -7.280109889 + -9 x = -7.280109889 + -9 Combine like terms: -7.280109889 + -9 = -16.280109889 x = -16.280109889 Simplifying x = -16.280109889Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.719890111, -16.280109889}Solution
x = {-1.719890111, -16.280109889}
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