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Simplifying 6x2 + -30x = 62 Reorder the terms: -30x + 6x2 = 62 Solving -30x + 6x2 = 62 Solving for variable 'x'. Reorder the terms: -62 + -30x + 6x2 = 62 + -62 Combine like terms: 62 + -62 = 0 -62 + -30x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-31 + -15x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-31 + -15x + 3x2)' equal to zero and attempt to solve: Simplifying -31 + -15x + 3x2 = 0 Solving -31 + -15x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -10.33333333 + -5x + x2 = 0 Move the constant term to the right: Add '10.33333333' to each side of the equation. -10.33333333 + -5x + 10.33333333 + x2 = 0 + 10.33333333 Reorder the terms: -10.33333333 + 10.33333333 + -5x + x2 = 0 + 10.33333333 Combine like terms: -10.33333333 + 10.33333333 = 0.00000000 0.00000000 + -5x + x2 = 0 + 10.33333333 -5x + x2 = 0 + 10.33333333 Combine like terms: 0 + 10.33333333 = 10.33333333 -5x + x2 = 10.33333333 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 10.33333333 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 10.33333333 + 6.25 Combine like terms: 10.33333333 + 6.25 = 16.58333333 6.25 + -5x + x2 = 16.58333333 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 16.58333333 Calculate the square root of the right side: 4.072263907 Break this problem into two subproblems by setting (x + -2.5) equal to 4.072263907 and -4.072263907.Subproblem 1
x + -2.5 = 4.072263907 Simplifying x + -2.5 = 4.072263907 Reorder the terms: -2.5 + x = 4.072263907 Solving -2.5 + x = 4.072263907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 4.072263907 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 4.072263907 + 2.5 x = 4.072263907 + 2.5 Combine like terms: 4.072263907 + 2.5 = 6.572263907 x = 6.572263907 Simplifying x = 6.572263907Subproblem 2
x + -2.5 = -4.072263907 Simplifying x + -2.5 = -4.072263907 Reorder the terms: -2.5 + x = -4.072263907 Solving -2.5 + x = -4.072263907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -4.072263907 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -4.072263907 + 2.5 x = -4.072263907 + 2.5 Combine like terms: -4.072263907 + 2.5 = -1.572263907 x = -1.572263907 Simplifying x = -1.572263907Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.572263907, -1.572263907}Solution
x = {6.572263907, -1.572263907}
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