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Simplifying (2x2 + -7x + -54) + (6x2 + 9x) = 0 Reorder the terms: (-54 + -7x + 2x2) + (6x2 + 9x) = 0 Remove parenthesis around (-54 + -7x + 2x2) -54 + -7x + 2x2 + (6x2 + 9x) = 0 Reorder the terms: -54 + -7x + 2x2 + (9x + 6x2) = 0 Remove parenthesis around (9x + 6x2) -54 + -7x + 2x2 + 9x + 6x2 = 0 Reorder the terms: -54 + -7x + 9x + 2x2 + 6x2 = 0 Combine like terms: -7x + 9x = 2x -54 + 2x + 2x2 + 6x2 = 0 Combine like terms: 2x2 + 6x2 = 8x2 -54 + 2x + 8x2 = 0 Solving -54 + 2x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-27 + x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-27 + x + 4x2)' equal to zero and attempt to solve: Simplifying -27 + x + 4x2 = 0 Solving -27 + x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.75 + 0.25x + x2 = 0 Move the constant term to the right: Add '6.75' to each side of the equation. -6.75 + 0.25x + 6.75 + x2 = 0 + 6.75 Reorder the terms: -6.75 + 6.75 + 0.25x + x2 = 0 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + 0.25x + x2 = 0 + 6.75 0.25x + x2 = 0 + 6.75 Combine like terms: 0 + 6.75 = 6.75 0.25x + x2 = 6.75 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.25x + 0.25 + x2 = 6.75 + 0.25 Reorder the terms: 0.25 + 0.25x + x2 = 6.75 + 0.25 Combine like terms: 6.75 + 0.25 = 7 0.25 + 0.25x + x2 = 7 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + 0.5) equal to 2.645751311 and -2.645751311.Subproblem 1
x + 0.5 = 2.645751311 Simplifying x + 0.5 = 2.645751311 Reorder the terms: 0.5 + x = 2.645751311 Solving 0.5 + x = 2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.645751311 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.645751311 + -0.5 x = 2.645751311 + -0.5 Combine like terms: 2.645751311 + -0.5 = 2.145751311 x = 2.145751311 Simplifying x = 2.145751311Subproblem 2
x + 0.5 = -2.645751311 Simplifying x + 0.5 = -2.645751311 Reorder the terms: 0.5 + x = -2.645751311 Solving 0.5 + x = -2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.645751311 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.645751311 + -0.5 x = -2.645751311 + -0.5 Combine like terms: -2.645751311 + -0.5 = -3.145751311 x = -3.145751311 Simplifying x = -3.145751311Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.145751311, -3.145751311}Solution
x = {2.145751311, -3.145751311}
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