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Simplifying 3x2 = 9x2 + -72x + 144 Reorder the terms: 3x2 = 144 + -72x + 9x2 Solving 3x2 = 144 + -72x + 9x2 Solving for variable 'x'. Reorder the terms: -144 + 72x + 3x2 + -9x2 = 144 + -72x + 9x2 + -144 + 72x + -9x2 Combine like terms: 3x2 + -9x2 = -6x2 -144 + 72x + -6x2 = 144 + -72x + 9x2 + -144 + 72x + -9x2 Reorder the terms: -144 + 72x + -6x2 = 144 + -144 + -72x + 72x + 9x2 + -9x2 Combine like terms: 144 + -144 = 0 -144 + 72x + -6x2 = 0 + -72x + 72x + 9x2 + -9x2 -144 + 72x + -6x2 = -72x + 72x + 9x2 + -9x2 Combine like terms: -72x + 72x = 0 -144 + 72x + -6x2 = 0 + 9x2 + -9x2 -144 + 72x + -6x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -144 + 72x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-24 + 12x + -1x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-24 + 12x + -1x2)' equal to zero and attempt to solve: Simplifying -24 + 12x + -1x2 = 0 Solving -24 + 12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 24 + -12x + x2 = 0 Move the constant term to the right: Add '-24' to each side of the equation. 24 + -12x + -24 + x2 = 0 + -24 Reorder the terms: 24 + -24 + -12x + x2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -12x + x2 = 0 + -24 -12x + x2 = 0 + -24 Combine like terms: 0 + -24 = -24 -12x + x2 = -24 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 = -24 + 36 Reorder the terms: 36 + -12x + x2 = -24 + 36 Combine like terms: -24 + 36 = 12 36 + -12x + x2 = 12 Factor a perfect square on the left side: (x + -6)(x + -6) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x + -6) equal to 3.464101615 and -3.464101615.Subproblem 1
x + -6 = 3.464101615 Simplifying x + -6 = 3.464101615 Reorder the terms: -6 + x = 3.464101615 Solving -6 + x = 3.464101615 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 = 3.464101615 + 6 Combine like terms: -6 + 6 = 0 0 + x = 3.464101615 + 6 x = 3.464101615 + 6 Combine like terms: 3.464101615 + 6 = 9.464101615 x = 9.464101615 Simplifying x = 9.464101615Subproblem 2
x + -6 = -3.464101615 Simplifying x + -6 = -3.464101615 Reorder the terms: -6 + x = -3.464101615 Solving -6 + x = -3.464101615 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 = -3.464101615 + 6 Combine like terms: -6 + 6 = 0 0 + x = -3.464101615 + 6 x = -3.464101615 + 6 Combine like terms: -3.464101615 + 6 = 2.535898385 x = 2.535898385 Simplifying x = 2.535898385Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.464101615, 2.535898385}Solution
x = {9.464101615, 2.535898385}
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