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Simplifying (x + 2)(2x + -5) = 54 Reorder the terms: (2 + x)(2x + -5) = 54 Reorder the terms: (2 + x)(-5 + 2x) = 54 Multiply (2 + x) * (-5 + 2x) (2(-5 + 2x) + x(-5 + 2x)) = 54 ((-5 * 2 + 2x * 2) + x(-5 + 2x)) = 54 ((-10 + 4x) + x(-5 + 2x)) = 54 (-10 + 4x + (-5 * x + 2x * x)) = 54 (-10 + 4x + (-5x + 2x2)) = 54 Combine like terms: 4x + -5x = -1x (-10 + -1x + 2x2) = 54 Solving -10 + -1x + 2x2 = 54 Solving for variable 'x'. Reorder the terms: -10 + -54 + -1x + 2x2 = 54 + -54 Combine like terms: -10 + -54 = -64 -64 + -1x + 2x2 = 54 + -54 Combine like terms: 54 + -54 = 0 -64 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -32 + -0.5x + x2 = 0 Move the constant term to the right: Add '32' to each side of the equation. -32 + -0.5x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + -0.5x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -0.5x + x2 = 0 + 32 -0.5x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 -0.5x + x2 = 32 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 32 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 32 + 0.0625 Combine like terms: 32 + 0.0625 = 32.0625 0.0625 + -0.5x + x2 = 32.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 32.0625 Calculate the square root of the right side: 5.662375826 Break this problem into two subproblems by setting (x + -0.25) equal to 5.662375826 and -5.662375826.Subproblem 1
x + -0.25 = 5.662375826 Simplifying x + -0.25 = 5.662375826 Reorder the terms: -0.25 + x = 5.662375826 Solving -0.25 + x = 5.662375826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 5.662375826 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 5.662375826 + 0.25 x = 5.662375826 + 0.25 Combine like terms: 5.662375826 + 0.25 = 5.912375826 x = 5.912375826 Simplifying x = 5.912375826Subproblem 2
x + -0.25 = -5.662375826 Simplifying x + -0.25 = -5.662375826 Reorder the terms: -0.25 + x = -5.662375826 Solving -0.25 + x = -5.662375826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -5.662375826 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -5.662375826 + 0.25 x = -5.662375826 + 0.25 Combine like terms: -5.662375826 + 0.25 = -5.412375826 x = -5.412375826 Simplifying x = -5.412375826Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.912375826, -5.412375826}
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