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Simplifying -3x(1x + -7) = -6 Reorder the terms: -3x(-7 + 1x) = -6 (-7 * -3x + 1x * -3x) = -6 (21x + -3x2) = -6 Solving 21x + -3x2 = -6 Solving for variable 'x'. Reorder the terms: 6 + 21x + -3x2 = -6 + 6 Combine like terms: -6 + 6 = 0 6 + 21x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(2 + 7x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2 + 7x + -1x2)' equal to zero and attempt to solve: Simplifying 2 + 7x + -1x2 = 0 Solving 2 + 7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + -7x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -7x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -7x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -7x + x2 = 0 + 2 -7x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -7x + x2 = 2 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 2 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 2 + 12.25 Combine like terms: 2 + 12.25 = 14.25 12.25 + -7x + x2 = 14.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (x + -3.5) equal to 3.774917218 and -3.774917218.Subproblem 1
x + -3.5 = 3.774917218 Simplifying x + -3.5 = 3.774917218 Reorder the terms: -3.5 + x = 3.774917218 Solving -3.5 + x = 3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 3.774917218 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.774917218 + 3.5 x = 3.774917218 + 3.5 Combine like terms: 3.774917218 + 3.5 = 7.274917218 x = 7.274917218 Simplifying x = 7.274917218Subproblem 2
x + -3.5 = -3.774917218 Simplifying x + -3.5 = -3.774917218 Reorder the terms: -3.5 + x = -3.774917218 Solving -3.5 + x = -3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -3.774917218 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.774917218 + 3.5 x = -3.774917218 + 3.5 Combine like terms: -3.774917218 + 3.5 = -0.274917218 x = -0.274917218 Simplifying x = -0.274917218Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.274917218, -0.274917218}Solution
x = {7.274917218, -0.274917218}
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