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Simplifying 42x2 + -496x + -2310 = 0 Reorder the terms: -2310 + -496x + 42x2 = 0 Solving -2310 + -496x + 42x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1155 + -248x + 21x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1155 + -248x + 21x2)' equal to zero and attempt to solve: Simplifying -1155 + -248x + 21x2 = 0 Solving -1155 + -248x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -55 + -11.80952381x + x2 = 0 Move the constant term to the right: Add '55' to each side of the equation. -55 + -11.80952381x + 55 + x2 = 0 + 55 Reorder the terms: -55 + 55 + -11.80952381x + x2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + -11.80952381x + x2 = 0 + 55 -11.80952381x + x2 = 0 + 55 Combine like terms: 0 + 55 = 55 -11.80952381x + x2 = 55 The x term is -11.80952381x. Take half its coefficient (-5.904761905). Square it (34.86621315) and add it to both sides. Add '34.86621315' to each side of the equation. -11.80952381x + 34.86621315 + x2 = 55 + 34.86621315 Reorder the terms: 34.86621315 + -11.80952381x + x2 = 55 + 34.86621315 Combine like terms: 55 + 34.86621315 = 89.86621315 34.86621315 + -11.80952381x + x2 = 89.86621315 Factor a perfect square on the left side: (x + -5.904761905)(x + -5.904761905) = 89.86621315 Calculate the square root of the right side: 9.479779172 Break this problem into two subproblems by setting (x + -5.904761905) equal to 9.479779172 and -9.479779172.Subproblem 1
x + -5.904761905 = 9.479779172 Simplifying x + -5.904761905 = 9.479779172 Reorder the terms: -5.904761905 + x = 9.479779172 Solving -5.904761905 + x = 9.479779172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.904761905' to each side of the equation. -5.904761905 + 5.904761905 + x = 9.479779172 + 5.904761905 Combine like terms: -5.904761905 + 5.904761905 = 0.000000000 0.000000000 + x = 9.479779172 + 5.904761905 x = 9.479779172 + 5.904761905 Combine like terms: 9.479779172 + 5.904761905 = 15.384541077 x = 15.384541077 Simplifying x = 15.384541077Subproblem 2
x + -5.904761905 = -9.479779172 Simplifying x + -5.904761905 = -9.479779172 Reorder the terms: -5.904761905 + x = -9.479779172 Solving -5.904761905 + x = -9.479779172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.904761905' to each side of the equation. -5.904761905 + 5.904761905 + x = -9.479779172 + 5.904761905 Combine like terms: -5.904761905 + 5.904761905 = 0.000000000 0.000000000 + x = -9.479779172 + 5.904761905 x = -9.479779172 + 5.904761905 Combine like terms: -9.479779172 + 5.904761905 = -3.575017267 x = -3.575017267 Simplifying x = -3.575017267Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.384541077, -3.575017267}Solution
x = {15.384541077, -3.575017267}
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