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Simplifying 5x2 + 45x + 65 = 0 Reorder the terms: 65 + 45x + 5x2 = 0 Solving 65 + 45x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(13 + 9x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(13 + 9x + x2)' equal to zero and attempt to solve: Simplifying 13 + 9x + x2 = 0 Solving 13 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + 9x + -13 + x2 = 0 + -13 Reorder the terms: 13 + -13 + 9x + x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 9x + x2 = 0 + -13 9x + x2 = 0 + -13 Combine like terms: 0 + -13 = -13 9x + x2 = -13 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = -13 + 20.25 Reorder the terms: 20.25 + 9x + x2 = -13 + 20.25 Combine like terms: -13 + 20.25 = 7.25 20.25 + 9x + x2 = 7.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (x + 4.5) equal to 2.692582404 and -2.692582404.Subproblem 1
x + 4.5 = 2.692582404 Simplifying x + 4.5 = 2.692582404 Reorder the terms: 4.5 + x = 2.692582404 Solving 4.5 + x = 2.692582404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 2.692582404 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 2.692582404 + -4.5 x = 2.692582404 + -4.5 Combine like terms: 2.692582404 + -4.5 = -1.807417596 x = -1.807417596 Simplifying x = -1.807417596Subproblem 2
x + 4.5 = -2.692582404 Simplifying x + 4.5 = -2.692582404 Reorder the terms: 4.5 + x = -2.692582404 Solving 4.5 + x = -2.692582404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -2.692582404 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -2.692582404 + -4.5 x = -2.692582404 + -4.5 Combine like terms: -2.692582404 + -4.5 = -7.192582404 x = -7.192582404 Simplifying x = -7.192582404Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.807417596, -7.192582404}Solution
x = {-1.807417596, -7.192582404}
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