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Simplifying 2x2 + 14x + -9 = -4x + 27x + 54 Reorder the terms: -9 + 14x + 2x2 = -4x + 27x + 54 Reorder the terms: -9 + 14x + 2x2 = 54 + -4x + 27x Combine like terms: -4x + 27x = 23x -9 + 14x + 2x2 = 54 + 23x Solving -9 + 14x + 2x2 = 54 + 23x Solving for variable 'x'. Reorder the terms: -9 + -54 + 14x + -23x + 2x2 = 54 + 23x + -54 + -23x Combine like terms: -9 + -54 = -63 -63 + 14x + -23x + 2x2 = 54 + 23x + -54 + -23x Combine like terms: 14x + -23x = -9x -63 + -9x + 2x2 = 54 + 23x + -54 + -23x Reorder the terms: -63 + -9x + 2x2 = 54 + -54 + 23x + -23x Combine like terms: 54 + -54 = 0 -63 + -9x + 2x2 = 0 + 23x + -23x -63 + -9x + 2x2 = 23x + -23x Combine like terms: 23x + -23x = 0 -63 + -9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -31.5 + -4.5x + x2 = 0 Move the constant term to the right: Add '31.5' to each side of the equation. -31.5 + -4.5x + 31.5 + x2 = 0 + 31.5 Reorder the terms: -31.5 + 31.5 + -4.5x + x2 = 0 + 31.5 Combine like terms: -31.5 + 31.5 = 0.0 0.0 + -4.5x + x2 = 0 + 31.5 -4.5x + x2 = 0 + 31.5 Combine like terms: 0 + 31.5 = 31.5 -4.5x + x2 = 31.5 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = 31.5 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 31.5 + 5.0625 Combine like terms: 31.5 + 5.0625 = 36.5625 5.0625 + -4.5x + x2 = 36.5625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 36.5625 Calculate the square root of the right side: 6.046693311 Break this problem into two subproblems by setting (x + -2.25) equal to 6.046693311 and -6.046693311.Subproblem 1
x + -2.25 = 6.046693311 Simplifying x + -2.25 = 6.046693311 Reorder the terms: -2.25 + x = 6.046693311 Solving -2.25 + x = 6.046693311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 6.046693311 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 6.046693311 + 2.25 x = 6.046693311 + 2.25 Combine like terms: 6.046693311 + 2.25 = 8.296693311 x = 8.296693311 Simplifying x = 8.296693311Subproblem 2
x + -2.25 = -6.046693311 Simplifying x + -2.25 = -6.046693311 Reorder the terms: -2.25 + x = -6.046693311 Solving -2.25 + x = -6.046693311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -6.046693311 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -6.046693311 + 2.25 x = -6.046693311 + 2.25 Combine like terms: -6.046693311 + 2.25 = -3.796693311 x = -3.796693311 Simplifying x = -3.796693311Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.296693311, -3.796693311}
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