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Simplifying 2x2 + -18x + -30 = 0 Reorder the terms: -30 + -18x + 2x2 = 0 Solving -30 + -18x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + -9x + x2) = 0 Ignore the factor 2.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 = 10.437171044 x = 10.437171044 Simplifying x = 10.437171044Subproblem 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 = -1.437171044 x = -1.437171044 Simplifying x = -1.437171044Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.437171044, -1.437171044}Solution
x = {10.437171044, -1.437171044}
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