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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 = 5.25 20.25 + -9x + x2 = 5.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (x + -4.5) equal to 2.291287847 and -2.291287847.Subproblem 1
x + -4.5 = 2.291287847 Simplifying x + -4.5 = 2.291287847 Reorder the terms: -4.5 + x = 2.291287847 Solving -4.5 + x = 2.291287847 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 = 2.291287847 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 2.291287847 + 4.5 x = 2.291287847 + 4.5 Combine like terms: 2.291287847 + 4.5 = 6.791287847 x = 6.791287847 Simplifying x = 6.791287847Subproblem 2
x + -4.5 = -2.291287847 Simplifying x + -4.5 = -2.291287847 Reorder the terms: -4.5 + x = -2.291287847 Solving -4.5 + x = -2.291287847 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 = -2.291287847 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -2.291287847 + 4.5 x = -2.291287847 + 4.5 Combine like terms: -2.291287847 + 4.5 = 2.208712153 x = 2.208712153 Simplifying x = 2.208712153Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.791287847, 2.208712153}Solution
x = {6.791287847, 2.208712153}
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