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Simplifying 4x2 + 6x + -72 = 0 Reorder the terms: -72 + 6x + 4x2 = 0 Solving -72 + 6x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-36 + 3x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-36 + 3x + 2x2)' equal to zero and attempt to solve: Simplifying -36 + 3x + 2x2 = 0 Solving -36 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -18 + 1.5x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + 1.5x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + 1.5x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 1.5x + x2 = 0 + 18 1.5x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 1.5x + x2 = 18 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 18 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 18 + 0.5625 Combine like terms: 18 + 0.5625 = 18.5625 0.5625 + 1.5x + x2 = 18.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 18.5625 Calculate the square root of the right side: 4.308421985 Break this problem into two subproblems by setting (x + 0.75) equal to 4.308421985 and -4.308421985.Subproblem 1
x + 0.75 = 4.308421985 Simplifying x + 0.75 = 4.308421985 Reorder the terms: 0.75 + x = 4.308421985 Solving 0.75 + x = 4.308421985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 4.308421985 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 4.308421985 + -0.75 x = 4.308421985 + -0.75 Combine like terms: 4.308421985 + -0.75 = 3.558421985 x = 3.558421985 Simplifying x = 3.558421985Subproblem 2
x + 0.75 = -4.308421985 Simplifying x + 0.75 = -4.308421985 Reorder the terms: 0.75 + x = -4.308421985 Solving 0.75 + x = -4.308421985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -4.308421985 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -4.308421985 + -0.75 x = -4.308421985 + -0.75 Combine like terms: -4.308421985 + -0.75 = -5.058421985 x = -5.058421985 Simplifying x = -5.058421985Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.558421985, -5.058421985}Solution
x = {3.558421985, -5.058421985}
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