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Simplifying 2x2 + -30x + 12 = 0 Reorder the terms: 12 + -30x + 2x2 = 0 Solving 12 + -30x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + -15x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + -15x + x2)' equal to zero and attempt to solve: Simplifying 6 + -15x + x2 = 0 Solving 6 + -15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -15x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -15x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -15x + x2 = 0 + -6 -15x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -15x + x2 = -6 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -6 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -6 + 56.25 Combine like terms: -6 + 56.25 = 50.25 56.25 + -15x + x2 = 50.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 50.25 Calculate the square root of the right side: 7.088723439 Break this problem into two subproblems by setting (x + -7.5) equal to 7.088723439 and -7.088723439.Subproblem 1
x + -7.5 = 7.088723439 Simplifying x + -7.5 = 7.088723439 Reorder the terms: -7.5 + x = 7.088723439 Solving -7.5 + x = 7.088723439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 7.088723439 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 7.088723439 + 7.5 x = 7.088723439 + 7.5 Combine like terms: 7.088723439 + 7.5 = 14.588723439 x = 14.588723439 Simplifying x = 14.588723439Subproblem 2
x + -7.5 = -7.088723439 Simplifying x + -7.5 = -7.088723439 Reorder the terms: -7.5 + x = -7.088723439 Solving -7.5 + x = -7.088723439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -7.088723439 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -7.088723439 + 7.5 x = -7.088723439 + 7.5 Combine like terms: -7.088723439 + 7.5 = 0.411276561 x = 0.411276561 Simplifying x = 0.411276561Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.588723439, 0.411276561}Solution
x = {14.588723439, 0.411276561}
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