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Simplifying 6x2 + 12x + -34 = 0 Reorder the terms: -34 + 12x + 6x2 = 0 Solving -34 + 12x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-17 + 6x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-17 + 6x + 3x2)' equal to zero and attempt to solve: Simplifying -17 + 6x + 3x2 = 0 Solving -17 + 6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5.666666667 + 2x + x2 = 0 Move the constant term to the right: Add '5.666666667' to each side of the equation. -5.666666667 + 2x + 5.666666667 + x2 = 0 + 5.666666667 Reorder the terms: -5.666666667 + 5.666666667 + 2x + x2 = 0 + 5.666666667 Combine like terms: -5.666666667 + 5.666666667 = 0.000000000 0.000000000 + 2x + x2 = 0 + 5.666666667 2x + x2 = 0 + 5.666666667 Combine like terms: 0 + 5.666666667 = 5.666666667 2x + x2 = 5.666666667 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 5.666666667 + 1 Reorder the terms: 1 + 2x + x2 = 5.666666667 + 1 Combine like terms: 5.666666667 + 1 = 6.666666667 1 + 2x + x2 = 6.666666667 Factor a perfect square on the left side: (x + 1)(x + 1) = 6.666666667 Calculate the square root of the right side: 2.581988898 Break this problem into two subproblems by setting (x + 1) equal to 2.581988898 and -2.581988898.Subproblem 1
x + 1 = 2.581988898 Simplifying x + 1 = 2.581988898 Reorder the terms: 1 + x = 2.581988898 Solving 1 + x = 2.581988898 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2.581988898 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.581988898 + -1 x = 2.581988898 + -1 Combine like terms: 2.581988898 + -1 = 1.581988898 x = 1.581988898 Simplifying x = 1.581988898Subproblem 2
x + 1 = -2.581988898 Simplifying x + 1 = -2.581988898 Reorder the terms: 1 + x = -2.581988898 Solving 1 + x = -2.581988898 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2.581988898 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.581988898 + -1 x = -2.581988898 + -1 Combine like terms: -2.581988898 + -1 = -3.581988898 x = -3.581988898 Simplifying x = -3.581988898Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.581988898, -3.581988898}Solution
x = {1.581988898, -3.581988898}
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