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Simplifying 4x2 + -12x = 180 Reorder the terms: -12x + 4x2 = 180 Solving -12x + 4x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + -12x + 4x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -12x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-45 + -3x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-45 + -3x + x2)' equal to zero and attempt to solve: Simplifying -45 + -3x + x2 = 0 Solving -45 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + -3x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + -3x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -3x + x2 = 0 + 45 -3x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 -3x + x2 = 45 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 45 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 45 + 2.25 Combine like terms: 45 + 2.25 = 47.25 2.25 + -3x + x2 = 47.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 47.25 Calculate the square root of the right side: 6.873863542 Break this problem into two subproblems by setting (x + -1.5) equal to 6.873863542 and -6.873863542.Subproblem 1
x + -1.5 = 6.873863542 Simplifying x + -1.5 = 6.873863542 Reorder the terms: -1.5 + x = 6.873863542 Solving -1.5 + x = 6.873863542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 6.873863542 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 6.873863542 + 1.5 x = 6.873863542 + 1.5 Combine like terms: 6.873863542 + 1.5 = 8.373863542 x = 8.373863542 Simplifying x = 8.373863542Subproblem 2
x + -1.5 = -6.873863542 Simplifying x + -1.5 = -6.873863542 Reorder the terms: -1.5 + x = -6.873863542 Solving -1.5 + x = -6.873863542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -6.873863542 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -6.873863542 + 1.5 x = -6.873863542 + 1.5 Combine like terms: -6.873863542 + 1.5 = -5.373863542 x = -5.373863542 Simplifying x = -5.373863542Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.373863542, -5.373863542}Solution
x = {8.373863542, -5.373863542}
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