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Simplifying 36x + 45 + -3x2 = 0 Reorder the terms: 45 + 36x + -3x2 = 0 Solving 45 + 36x + -3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(15 + 12x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(15 + 12x + -1x2)' equal to zero and attempt to solve: Simplifying 15 + 12x + -1x2 = 0 Solving 15 + 12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -15 + -12x + x2 = 0 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 = 13.141428429 x = 13.141428429 Simplifying x = 13.141428429Subproblem 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 = -1.141428429 x = -1.141428429 Simplifying x = -1.141428429Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.141428429, -1.141428429}Solution
x = {13.141428429, -1.141428429}
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