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Simplifying 6x2 + -90x + 252 = 0 Reorder the terms: 252 + -90x + 6x2 = 0 Solving 252 + -90x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(42 + -15x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(42 + -15x + x2)' equal to zero and attempt to solve: Simplifying 42 + -15x + x2 = 0 Solving 42 + -15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-42' to each side of the equation. 42 + -15x + -42 + x2 = 0 + -42 Reorder the terms: 42 + -42 + -15x + x2 = 0 + -42 Combine like terms: 42 + -42 = 0 0 + -15x + x2 = 0 + -42 -15x + x2 = 0 + -42 Combine like terms: 0 + -42 = -42 -15x + x2 = -42 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 = -42 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -42 + 56.25 Combine like terms: -42 + 56.25 = 14.25 56.25 + -15x + x2 = 14.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (x + -7.5) equal to 3.774917218 and -3.774917218.Subproblem 1
x + -7.5 = 3.774917218 Simplifying x + -7.5 = 3.774917218 Reorder the terms: -7.5 + x = 3.774917218 Solving -7.5 + x = 3.774917218 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 = 3.774917218 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 3.774917218 + 7.5 x = 3.774917218 + 7.5 Combine like terms: 3.774917218 + 7.5 = 11.274917218 x = 11.274917218 Simplifying x = 11.274917218Subproblem 2
x + -7.5 = -3.774917218 Simplifying x + -7.5 = -3.774917218 Reorder the terms: -7.5 + x = -3.774917218 Solving -7.5 + x = -3.774917218 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 = -3.774917218 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -3.774917218 + 7.5 x = -3.774917218 + 7.5 Combine like terms: -3.774917218 + 7.5 = 3.725082782 x = 3.725082782 Simplifying x = 3.725082782Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.274917218, 3.725082782}Solution
x = {11.274917218, 3.725082782}
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