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Simplifying 5x2 = 120 + 5x Solving 5x2 = 120 + 5x Solving for variable 'x'. Reorder the terms: -120 + -5x + 5x2 = 120 + 5x + -120 + -5x Reorder the terms: -120 + -5x + 5x2 = 120 + -120 + 5x + -5x Combine like terms: 120 + -120 = 0 -120 + -5x + 5x2 = 0 + 5x + -5x -120 + -5x + 5x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -120 + -5x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-24 + -1x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-24 + -1x + x2)' equal to zero and attempt to solve: Simplifying -24 + -1x + x2 = 0 Solving -24 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + -1x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + -1x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -1x + x2 = 0 + 24 -1x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 -1x + x2 = 24 The x term is -1x. 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. -1x + 0.25 + x2 = 24 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 24 + 0.25 Combine like terms: 24 + 0.25 = 24.25 0.25 + -1x + x2 = 24.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (x + -0.5) equal to 4.924428901 and -4.924428901.Subproblem 1
x + -0.5 = 4.924428901 Simplifying x + -0.5 = 4.924428901 Reorder the terms: -0.5 + x = 4.924428901 Solving -0.5 + x = 4.924428901 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 = 4.924428901 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 4.924428901 + 0.5 x = 4.924428901 + 0.5 Combine like terms: 4.924428901 + 0.5 = 5.424428901 x = 5.424428901 Simplifying x = 5.424428901Subproblem 2
x + -0.5 = -4.924428901 Simplifying x + -0.5 = -4.924428901 Reorder the terms: -0.5 + x = -4.924428901 Solving -0.5 + x = -4.924428901 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 = -4.924428901 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -4.924428901 + 0.5 x = -4.924428901 + 0.5 Combine like terms: -4.924428901 + 0.5 = -4.424428901 x = -4.424428901 Simplifying x = -4.424428901Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.424428901, -4.424428901}Solution
x = {5.424428901, -4.424428901}
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