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Simplifying 6x2 + -87x + 12 = 0 Reorder the terms: 12 + -87x + 6x2 = 0 Solving 12 + -87x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(4 + -29x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + -29x + 2x2)' equal to zero and attempt to solve: Simplifying 4 + -29x + 2x2 = 0 Solving 4 + -29x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2 + -14.5x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -14.5x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -14.5x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -14.5x + x2 = 0 + -2 -14.5x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -14.5x + x2 = -2 The x term is -14.5x. Take half its coefficient (-7.25). Square it (52.5625) and add it to both sides. Add '52.5625' to each side of the equation. -14.5x + 52.5625 + x2 = -2 + 52.5625 Reorder the terms: 52.5625 + -14.5x + x2 = -2 + 52.5625 Combine like terms: -2 + 52.5625 = 50.5625 52.5625 + -14.5x + x2 = 50.5625 Factor a perfect square on the left side: (x + -7.25)(x + -7.25) = 50.5625 Calculate the square root of the right side: 7.110731327 Break this problem into two subproblems by setting (x + -7.25) equal to 7.110731327 and -7.110731327.Subproblem 1
x + -7.25 = 7.110731327 Simplifying x + -7.25 = 7.110731327 Reorder the terms: -7.25 + x = 7.110731327 Solving -7.25 + x = 7.110731327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.25' to each side of the equation. -7.25 + 7.25 + x = 7.110731327 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + x = 7.110731327 + 7.25 x = 7.110731327 + 7.25 Combine like terms: 7.110731327 + 7.25 = 14.360731327 x = 14.360731327 Simplifying x = 14.360731327Subproblem 2
x + -7.25 = -7.110731327 Simplifying x + -7.25 = -7.110731327 Reorder the terms: -7.25 + x = -7.110731327 Solving -7.25 + x = -7.110731327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.25' to each side of the equation. -7.25 + 7.25 + x = -7.110731327 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + x = -7.110731327 + 7.25 x = -7.110731327 + 7.25 Combine like terms: -7.110731327 + 7.25 = 0.139268673 x = 0.139268673 Simplifying x = 0.139268673Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.360731327, 0.139268673}Solution
x = {14.360731327, 0.139268673}
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