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Simplifying 12x2 + -192x + 597 = 0 Reorder the terms: 597 + -192x + 12x2 = 0 Solving 597 + -192x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(199 + -64x + 4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(199 + -64x + 4x2)' equal to zero and attempt to solve: Simplifying 199 + -64x + 4x2 = 0 Solving 199 + -64x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 49.75 + -16x + x2 = 0 Move the constant term to the right: Add '-49.75' to each side of the equation. 49.75 + -16x + -49.75 + x2 = 0 + -49.75 Reorder the terms: 49.75 + -49.75 + -16x + x2 = 0 + -49.75 Combine like terms: 49.75 + -49.75 = 0.00 0.00 + -16x + x2 = 0 + -49.75 -16x + x2 = 0 + -49.75 Combine like terms: 0 + -49.75 = -49.75 -16x + x2 = -49.75 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = -49.75 + 64 Reorder the terms: 64 + -16x + x2 = -49.75 + 64 Combine like terms: -49.75 + 64 = 14.25 64 + -16x + x2 = 14.25 Factor a perfect square on the left side: (x + -8)(x + -8) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (x + -8) equal to 3.774917218 and -3.774917218.Subproblem 1
x + -8 = 3.774917218 Simplifying x + -8 = 3.774917218 Reorder the terms: -8 + x = 3.774917218 Solving -8 + x = 3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 3.774917218 + 8 Combine like terms: -8 + 8 = 0 0 + x = 3.774917218 + 8 x = 3.774917218 + 8 Combine like terms: 3.774917218 + 8 = 11.774917218 x = 11.774917218 Simplifying x = 11.774917218Subproblem 2
x + -8 = -3.774917218 Simplifying x + -8 = -3.774917218 Reorder the terms: -8 + x = -3.774917218 Solving -8 + x = -3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -3.774917218 + 8 Combine like terms: -8 + 8 = 0 0 + x = -3.774917218 + 8 x = -3.774917218 + 8 Combine like terms: -3.774917218 + 8 = 4.225082782 x = 4.225082782 Simplifying x = 4.225082782Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.774917218, 4.225082782}Solution
x = {11.774917218, 4.225082782}
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