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Simplifying 3(x2 + -30x + 39) = 0 Reorder the terms: 3(39 + -30x + x2) = 0 (39 * 3 + -30x * 3 + x2 * 3) = 0 (117 + -90x + 3x2) = 0 Solving 117 + -90x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(39 + -30x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(39 + -30x + x2)' equal to zero and attempt to solve: Simplifying 39 + -30x + x2 = 0 Solving 39 + -30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-39' to each side of the equation. 39 + -30x + -39 + x2 = 0 + -39 Reorder the terms: 39 + -39 + -30x + x2 = 0 + -39 Combine like terms: 39 + -39 = 0 0 + -30x + x2 = 0 + -39 -30x + x2 = 0 + -39 Combine like terms: 0 + -39 = -39 -30x + x2 = -39 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = -39 + 225 Reorder the terms: 225 + -30x + x2 = -39 + 225 Combine like terms: -39 + 225 = 186 225 + -30x + x2 = 186 Factor a perfect square on the left side: (x + -15)(x + -15) = 186 Calculate the square root of the right side: 13.638181697 Break this problem into two subproblems by setting (x + -15) equal to 13.638181697 and -13.638181697.Subproblem 1
x + -15 = 13.638181697 Simplifying x + -15 = 13.638181697 Reorder the terms: -15 + x = 13.638181697 Solving -15 + x = 13.638181697 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 13.638181697 + 15 Combine like terms: -15 + 15 = 0 0 + x = 13.638181697 + 15 x = 13.638181697 + 15 Combine like terms: 13.638181697 + 15 = 28.638181697 x = 28.638181697 Simplifying x = 28.638181697Subproblem 2
x + -15 = -13.638181697 Simplifying x + -15 = -13.638181697 Reorder the terms: -15 + x = -13.638181697 Solving -15 + x = -13.638181697 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -13.638181697 + 15 Combine like terms: -15 + 15 = 0 0 + x = -13.638181697 + 15 x = -13.638181697 + 15 Combine like terms: -13.638181697 + 15 = 1.361818303 x = 1.361818303 Simplifying x = 1.361818303Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.638181697, 1.361818303}Solution
x = {28.638181697, 1.361818303}
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