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Simplifying 12x2 + -42x + -240 = 0 Reorder the terms: -240 + -42x + 12x2 = 0 Solving -240 + -42x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-40 + -7x + 2x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-40 + -7x + 2x2)' equal to zero and attempt to solve: Simplifying -40 + -7x + 2x2 = 0 Solving -40 + -7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -20 + -3.5x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -3.5x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -3.5x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -3.5x + x2 = 0 + 20 -3.5x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -3.5x + x2 = 20 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 20 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 20 + 3.0625 Combine like terms: 20 + 3.0625 = 23.0625 3.0625 + -3.5x + x2 = 23.0625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 23.0625 Calculate the square root of the right side: 4.802343178 Break this problem into two subproblems by setting (x + -1.75) equal to 4.802343178 and -4.802343178.Subproblem 1
x + -1.75 = 4.802343178 Simplifying x + -1.75 = 4.802343178 Reorder the terms: -1.75 + x = 4.802343178 Solving -1.75 + x = 4.802343178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 4.802343178 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 4.802343178 + 1.75 x = 4.802343178 + 1.75 Combine like terms: 4.802343178 + 1.75 = 6.552343178 x = 6.552343178 Simplifying x = 6.552343178Subproblem 2
x + -1.75 = -4.802343178 Simplifying x + -1.75 = -4.802343178 Reorder the terms: -1.75 + x = -4.802343178 Solving -1.75 + x = -4.802343178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -4.802343178 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -4.802343178 + 1.75 x = -4.802343178 + 1.75 Combine like terms: -4.802343178 + 1.75 = -3.052343178 x = -3.052343178 Simplifying x = -3.052343178Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.552343178, -3.052343178}Solution
x = {6.552343178, -3.052343178}
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