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Simplifying 13x2 + 9x + -4 + -7x2 + 15x + -6 = 0 Reorder the terms: -4 + -6 + 9x + 15x + 13x2 + -7x2 = 0 Combine like terms: -4 + -6 = -10 -10 + 9x + 15x + 13x2 + -7x2 = 0 Combine like terms: 9x + 15x = 24x -10 + 24x + 13x2 + -7x2 = 0 Combine like terms: 13x2 + -7x2 = 6x2 -10 + 24x + 6x2 = 0 Solving -10 + 24x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 12x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 12x + 3x2)' equal to zero and attempt to solve: Simplifying -5 + 12x + 3x2 = 0 Solving -5 + 12x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.666666667 + 4x + x2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + 4x + 1.666666667 + x2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + 4x + x2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + 4x + x2 = 0 + 1.666666667 4x + x2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 4x + x2 = 1.666666667 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 = 1.666666667 + 4 Reorder the terms: 4 + 4x + x2 = 1.666666667 + 4 Combine like terms: 1.666666667 + 4 = 5.666666667 4 + 4x + x2 = 5.666666667 Factor a perfect square on the left side: (x + 2)(x + 2) = 5.666666667 Calculate the square root of the right side: 2.380476143 Break this problem into two subproblems by setting (x + 2) equal to 2.380476143 and -2.380476143.Subproblem 1
x + 2 = 2.380476143 Simplifying x + 2 = 2.380476143 Reorder the terms: 2 + x = 2.380476143 Solving 2 + x = 2.380476143 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 = 2.380476143 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.380476143 + -2 x = 2.380476143 + -2 Combine like terms: 2.380476143 + -2 = 0.380476143 x = 0.380476143 Simplifying x = 0.380476143Subproblem 2
x + 2 = -2.380476143 Simplifying x + 2 = -2.380476143 Reorder the terms: 2 + x = -2.380476143 Solving 2 + x = -2.380476143 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 = -2.380476143 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.380476143 + -2 x = -2.380476143 + -2 Combine like terms: -2.380476143 + -2 = -4.380476143 x = -4.380476143 Simplifying x = -4.380476143Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.380476143, -4.380476143}Solution
x = {0.380476143, -4.380476143}
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