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Simplifying 8x2 + 54x + 72 = 0 Reorder the terms: 72 + 54x + 8x2 = 0 Solving 72 + 54x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(36 + 27x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(36 + 27x + 4x2)' equal to zero and attempt to solve: Simplifying 36 + 27x + 4x2 = 0 Solving 36 + 27x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 9 + 6.75x + x2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + 6.75x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + 6.75x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 6.75x + x2 = 0 + -9 6.75x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 6.75x + x2 = -9 The x term is 6.75x. Take half its coefficient (3.375). Square it (11.390625) and add it to both sides. Add '11.390625' to each side of the equation. 6.75x + 11.390625 + x2 = -9 + 11.390625 Reorder the terms: 11.390625 + 6.75x + x2 = -9 + 11.390625 Combine like terms: -9 + 11.390625 = 2.390625 11.390625 + 6.75x + x2 = 2.390625 Factor a perfect square on the left side: (x + 3.375)(x + 3.375) = 2.390625 Calculate the square root of the right side: 1.54616461 Break this problem into two subproblems by setting (x + 3.375) equal to 1.54616461 and -1.54616461.Subproblem 1
x + 3.375 = 1.54616461 Simplifying x + 3.375 = 1.54616461 Reorder the terms: 3.375 + x = 1.54616461 Solving 3.375 + x = 1.54616461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.375' to each side of the equation. 3.375 + -3.375 + x = 1.54616461 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + x = 1.54616461 + -3.375 x = 1.54616461 + -3.375 Combine like terms: 1.54616461 + -3.375 = -1.82883539 x = -1.82883539 Simplifying x = -1.82883539Subproblem 2
x + 3.375 = -1.54616461 Simplifying x + 3.375 = -1.54616461 Reorder the terms: 3.375 + x = -1.54616461 Solving 3.375 + x = -1.54616461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.375' to each side of the equation. 3.375 + -3.375 + x = -1.54616461 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + x = -1.54616461 + -3.375 x = -1.54616461 + -3.375 Combine like terms: -1.54616461 + -3.375 = -4.92116461 x = -4.92116461 Simplifying x = -4.92116461Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.82883539, -4.92116461}Solution
x = {-1.82883539, -4.92116461}
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