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Simplifying 12x2 + 60x + -75 = 0 Reorder the terms: -75 + 60x + 12x2 = 0 Solving -75 + 60x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-25 + 20x + 4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-25 + 20x + 4x2)' equal to zero and attempt to solve: Simplifying -25 + 20x + 4x2 = 0 Solving -25 + 20x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.25 + 5x + x2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + 5x + 6.25 + x2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + 5x + x2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + 5x + x2 = 0 + 6.25 5x + x2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 5x + x2 = 6.25 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 = 6.25 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 6.25 + 6.25 Combine like terms: 6.25 + 6.25 = 12.5 6.25 + 5x + x2 = 12.5 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 12.5 Calculate the square root of the right side: 3.535533906 Break this problem into two subproblems by setting (x + 2.5) equal to 3.535533906 and -3.535533906.Subproblem 1
x + 2.5 = 3.535533906 Simplifying x + 2.5 = 3.535533906 Reorder the terms: 2.5 + x = 3.535533906 Solving 2.5 + x = 3.535533906 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 = 3.535533906 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 3.535533906 + -2.5 x = 3.535533906 + -2.5 Combine like terms: 3.535533906 + -2.5 = 1.035533906 x = 1.035533906 Simplifying x = 1.035533906Subproblem 2
x + 2.5 = -3.535533906 Simplifying x + 2.5 = -3.535533906 Reorder the terms: 2.5 + x = -3.535533906 Solving 2.5 + x = -3.535533906 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 = -3.535533906 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -3.535533906 + -2.5 x = -3.535533906 + -2.5 Combine like terms: -3.535533906 + -2.5 = -6.035533906 x = -6.035533906 Simplifying x = -6.035533906Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.035533906, -6.035533906}Solution
x = {1.035533906, -6.035533906}
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