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Simplifying 4x2 + -6x + -216 = 0 Reorder the terms: -216 + -6x + 4x2 = 0 Solving -216 + -6x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-108 + -3x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-108 + -3x + 2x2)' equal to zero and attempt to solve: Simplifying -108 + -3x + 2x2 = 0 Solving -108 + -3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -54 + -1.5x + x2 = 0 Move the constant term to the right: Add '54' to each side of the equation. -54 + -1.5x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + -1.5x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + -1.5x + x2 = 0 + 54 -1.5x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 -1.5x + x2 = 54 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 = 54 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 54 + 0.5625 Combine like terms: 54 + 0.5625 = 54.5625 0.5625 + -1.5x + x2 = 54.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 54.5625 Calculate the square root of the right side: 7.386643351 Break this problem into two subproblems by setting (x + -0.75) equal to 7.386643351 and -7.386643351.Subproblem 1
x + -0.75 = 7.386643351 Simplifying x + -0.75 = 7.386643351 Reorder the terms: -0.75 + x = 7.386643351 Solving -0.75 + x = 7.386643351 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 = 7.386643351 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 7.386643351 + 0.75 x = 7.386643351 + 0.75 Combine like terms: 7.386643351 + 0.75 = 8.136643351 x = 8.136643351 Simplifying x = 8.136643351Subproblem 2
x + -0.75 = -7.386643351 Simplifying x + -0.75 = -7.386643351 Reorder the terms: -0.75 + x = -7.386643351 Solving -0.75 + x = -7.386643351 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 = -7.386643351 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -7.386643351 + 0.75 x = -7.386643351 + 0.75 Combine like terms: -7.386643351 + 0.75 = -6.636643351 x = -6.636643351 Simplifying x = -6.636643351Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.136643351, -6.636643351}Solution
x = {8.136643351, -6.636643351}
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