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Simplifying 3x2 + 36x = 45 Reorder the terms: 36x + 3x2 = 45 Solving 36x + 3x2 = 45 Solving for variable 'x'. Reorder the terms: -45 + 36x + 3x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + 36x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-15 + 12x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-15 + 12x + x2)' equal to zero and attempt to solve: Simplifying -15 + 12x + x2 = 0 Solving -15 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 12x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 12x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 12x + x2 = 0 + 15 12x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 12x + x2 = 15 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 15 + 36 Reorder the terms: 36 + 12x + x2 = 15 + 36 Combine like terms: 15 + 36 = 51 36 + 12x + x2 = 51 Factor a perfect square on the left side: (x + 6)(x + 6) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (x + 6) equal to 7.141428429 and -7.141428429.Subproblem 1
x + 6 = 7.141428429 Simplifying x + 6 = 7.141428429 Reorder the terms: 6 + x = 7.141428429 Solving 6 + x = 7.141428429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 7.141428429 + -6 Combine like terms: 6 + -6 = 0 0 + x = 7.141428429 + -6 x = 7.141428429 + -6 Combine like terms: 7.141428429 + -6 = 1.141428429 x = 1.141428429 Simplifying x = 1.141428429Subproblem 2
x + 6 = -7.141428429 Simplifying x + 6 = -7.141428429 Reorder the terms: 6 + x = -7.141428429 Solving 6 + x = -7.141428429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -7.141428429 + -6 Combine like terms: 6 + -6 = 0 0 + x = -7.141428429 + -6 x = -7.141428429 + -6 Combine like terms: -7.141428429 + -6 = -13.141428429 x = -13.141428429 Simplifying x = -13.141428429Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.141428429, -13.141428429}Solution
x = {1.141428429, -13.141428429}
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