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Simplifying 0 = 6x2 + 24x + 17 Reorder the terms: 0 = 17 + 24x + 6x2 Solving 0 = 17 + 24x + 6x2 Solving for variable 'x'. Combine like terms: 0 + -17 = -17 -17 + -24x + -6x2 = 17 + 24x + 6x2 + -17 + -24x + -6x2 Reorder the terms: -17 + -24x + -6x2 = 17 + -17 + 24x + -24x + 6x2 + -6x2 Combine like terms: 17 + -17 = 0 -17 + -24x + -6x2 = 0 + 24x + -24x + 6x2 + -6x2 -17 + -24x + -6x2 = 24x + -24x + 6x2 + -6x2 Combine like terms: 24x + -24x = 0 -17 + -24x + -6x2 = 0 + 6x2 + -6x2 -17 + -24x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -17 + -24x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(17 + 24x + 6x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(17 + 24x + 6x2)' equal to zero and attempt to solve: Simplifying 17 + 24x + 6x2 = 0 Solving 17 + 24x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 2.833333333 + 4x + x2 = 0 Move the constant term to the right: Add '-2.833333333' to each side of the equation. 2.833333333 + 4x + -2.833333333 + x2 = 0 + -2.833333333 Reorder the terms: 2.833333333 + -2.833333333 + 4x + x2 = 0 + -2.833333333 Combine like terms: 2.833333333 + -2.833333333 = 0.000000000 0.000000000 + 4x + x2 = 0 + -2.833333333 4x + x2 = 0 + -2.833333333 Combine like terms: 0 + -2.833333333 = -2.833333333 4x + x2 = -2.833333333 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -2.833333333 + 4 Reorder the terms: 4 + 4x + x2 = -2.833333333 + 4 Combine like terms: -2.833333333 + 4 = 1.166666667 4 + 4x + x2 = 1.166666667 Factor a perfect square on the left side: (x + 2)(x + 2) = 1.166666667 Calculate the square root of the right side: 1.08012345 Break this problem into two subproblems by setting (x + 2) equal to 1.08012345 and -1.08012345.Subproblem 1
x + 2 = 1.08012345 Simplifying x + 2 = 1.08012345 Reorder the terms: 2 + x = 1.08012345 Solving 2 + x = 1.08012345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 1.08012345 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.08012345 + -2 x = 1.08012345 + -2 Combine like terms: 1.08012345 + -2 = -0.91987655 x = -0.91987655 Simplifying x = -0.91987655Subproblem 2
x + 2 = -1.08012345 Simplifying x + 2 = -1.08012345 Reorder the terms: 2 + x = -1.08012345 Solving 2 + x = -1.08012345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -1.08012345 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.08012345 + -2 x = -1.08012345 + -2 Combine like terms: -1.08012345 + -2 = -3.08012345 x = -3.08012345 Simplifying x = -3.08012345Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.91987655, -3.08012345}Solution
x = {-0.91987655, -3.08012345}
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