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Simplifying 4x2 + 36x + -60 = 0 Reorder the terms: -60 + 36x + 4x2 = 0 Solving -60 + 36x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-15 + 9x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-15 + 9x + x2)' equal to zero and attempt to solve: Simplifying -15 + 9x + x2 = 0 Solving -15 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 9x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 9x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 9x + x2 = 0 + 15 9x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 9x + x2 = 15 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 = 15 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 15 + 20.25 Combine like terms: 15 + 20.25 = 35.25 20.25 + 9x + x2 = 35.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 35.25 Calculate the square root of the right side: 5.937171044 Break this problem into two subproblems by setting (x + 4.5) equal to 5.937171044 and -5.937171044.Subproblem 1
x + 4.5 = 5.937171044 Simplifying x + 4.5 = 5.937171044 Reorder the terms: 4.5 + x = 5.937171044 Solving 4.5 + x = 5.937171044 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 = 5.937171044 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 5.937171044 + -4.5 x = 5.937171044 + -4.5 Combine like terms: 5.937171044 + -4.5 = 1.437171044 x = 1.437171044 Simplifying x = 1.437171044Subproblem 2
x + 4.5 = -5.937171044 Simplifying x + 4.5 = -5.937171044 Reorder the terms: 4.5 + x = -5.937171044 Solving 4.5 + x = -5.937171044 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 = -5.937171044 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -5.937171044 + -4.5 x = -5.937171044 + -4.5 Combine like terms: -5.937171044 + -4.5 = -10.437171044 x = -10.437171044 Simplifying x = -10.437171044Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.437171044, -10.437171044}Solution
x = {1.437171044, -10.437171044}
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