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Simplifying 6x2 + -6x = 57 Reorder the terms: -6x + 6x2 = 57 Solving -6x + 6x2 = 57 Solving for variable 'x'. Reorder the terms: -57 + -6x + 6x2 = 57 + -57 Combine like terms: 57 + -57 = 0 -57 + -6x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-19 + -2x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-19 + -2x + 2x2)' equal to zero and attempt to solve: Simplifying -19 + -2x + 2x2 = 0 Solving -19 + -2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -9.5 + -1x + x2 = 0 Move the constant term to the right: Add '9.5' to each side of the equation. -9.5 + -1x + 9.5 + x2 = 0 + 9.5 Reorder the terms: -9.5 + 9.5 + -1x + x2 = 0 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + -1x + x2 = 0 + 9.5 -1x + x2 = 0 + 9.5 Combine like terms: 0 + 9.5 = 9.5 -1x + x2 = 9.5 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 9.5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 9.5 + 0.25 Combine like terms: 9.5 + 0.25 = 9.75 0.25 + -1x + x2 = 9.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 9.75 Calculate the square root of the right side: 3.122498999 Break this problem into two subproblems by setting (x + -0.5) equal to 3.122498999 and -3.122498999.Subproblem 1
x + -0.5 = 3.122498999 Simplifying x + -0.5 = 3.122498999 Reorder the terms: -0.5 + x = 3.122498999 Solving -0.5 + x = 3.122498999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 3.122498999 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 3.122498999 + 0.5 x = 3.122498999 + 0.5 Combine like terms: 3.122498999 + 0.5 = 3.622498999 x = 3.622498999 Simplifying x = 3.622498999Subproblem 2
x + -0.5 = -3.122498999 Simplifying x + -0.5 = -3.122498999 Reorder the terms: -0.5 + x = -3.122498999 Solving -0.5 + x = -3.122498999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -3.122498999 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -3.122498999 + 0.5 x = -3.122498999 + 0.5 Combine like terms: -3.122498999 + 0.5 = -2.622498999 x = -2.622498999 Simplifying x = -2.622498999Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.622498999, -2.622498999}Solution
x = {3.622498999, -2.622498999}
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