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Simplifying 0 = 2x2 + 6x + -144 Reorder the terms: 0 = -144 + 6x + 2x2 Solving 0 = -144 + 6x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 144 = 144 144 + -6x + -2x2 = -144 + 6x + 2x2 + 144 + -6x + -2x2 Reorder the terms: 144 + -6x + -2x2 = -144 + 144 + 6x + -6x + 2x2 + -2x2 Combine like terms: -144 + 144 = 0 144 + -6x + -2x2 = 0 + 6x + -6x + 2x2 + -2x2 144 + -6x + -2x2 = 6x + -6x + 2x2 + -2x2 Combine like terms: 6x + -6x = 0 144 + -6x + -2x2 = 0 + 2x2 + -2x2 144 + -6x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 144 + -6x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(72 + -3x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(72 + -3x + -1x2)' equal to zero and attempt to solve: Simplifying 72 + -3x + -1x2 = 0 Solving 72 + -3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -72 + 3x + x2 = 0 Move the constant term to the right: Add '72' to each side of the equation. -72 + 3x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + 3x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 3x + x2 = 0 + 72 3x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 3x + x2 = 72 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 72 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 72 + 2.25 Combine like terms: 72 + 2.25 = 74.25 2.25 + 3x + x2 = 74.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 74.25 Calculate the square root of the right side: 8.61684397 Break this problem into two subproblems by setting (x + 1.5) equal to 8.61684397 and -8.61684397.Subproblem 1
x + 1.5 = 8.61684397 Simplifying x + 1.5 = 8.61684397 Reorder the terms: 1.5 + x = 8.61684397 Solving 1.5 + x = 8.61684397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 8.61684397 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 8.61684397 + -1.5 x = 8.61684397 + -1.5 Combine like terms: 8.61684397 + -1.5 = 7.11684397 x = 7.11684397 Simplifying x = 7.11684397Subproblem 2
x + 1.5 = -8.61684397 Simplifying x + 1.5 = -8.61684397 Reorder the terms: 1.5 + x = -8.61684397 Solving 1.5 + x = -8.61684397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -8.61684397 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -8.61684397 + -1.5 x = -8.61684397 + -1.5 Combine like terms: -8.61684397 + -1.5 = -10.11684397 x = -10.11684397 Simplifying x = -10.11684397Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.11684397, -10.11684397}Solution
x = {7.11684397, -10.11684397}
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