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Simplifying (6x2 + -7x + -26) + (4x2 + 9x) = 0 Reorder the terms: (-26 + -7x + 6x2) + (4x2 + 9x) = 0 Remove parenthesis around (-26 + -7x + 6x2) -26 + -7x + 6x2 + (4x2 + 9x) = 0 Reorder the terms: -26 + -7x + 6x2 + (9x + 4x2) = 0 Remove parenthesis around (9x + 4x2) -26 + -7x + 6x2 + 9x + 4x2 = 0 Reorder the terms: -26 + -7x + 9x + 6x2 + 4x2 = 0 Combine like terms: -7x + 9x = 2x -26 + 2x + 6x2 + 4x2 = 0 Combine like terms: 6x2 + 4x2 = 10x2 -26 + 2x + 10x2 = 0 Solving -26 + 2x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-13 + x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-13 + x + 5x2)' equal to zero and attempt to solve: Simplifying -13 + x + 5x2 = 0 Solving -13 + x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.6 + 0.2x + x2 = 0 Move the constant term to the right: Add '2.6' to each side of the equation. -2.6 + 0.2x + 2.6 + x2 = 0 + 2.6 Reorder the terms: -2.6 + 2.6 + 0.2x + x2 = 0 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + 0.2x + x2 = 0 + 2.6 0.2x + x2 = 0 + 2.6 Combine like terms: 0 + 2.6 = 2.6 0.2x + x2 = 2.6 The x term is x. 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. 0.2x + 0.25 + x2 = 2.6 + 0.25 Reorder the terms: 0.25 + 0.2x + x2 = 2.6 + 0.25 Combine like terms: 2.6 + 0.25 = 2.85 0.25 + 0.2x + x2 = 2.85 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.85 Calculate the square root of the right side: 1.688194302 Break this problem into two subproblems by setting (x + 0.5) equal to 1.688194302 and -1.688194302.Subproblem 1
x + 0.5 = 1.688194302 Simplifying x + 0.5 = 1.688194302 Reorder the terms: 0.5 + x = 1.688194302 Solving 0.5 + x = 1.688194302 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 = 1.688194302 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.688194302 + -0.5 x = 1.688194302 + -0.5 Combine like terms: 1.688194302 + -0.5 = 1.188194302 x = 1.188194302 Simplifying x = 1.188194302Subproblem 2
x + 0.5 = -1.688194302 Simplifying x + 0.5 = -1.688194302 Reorder the terms: 0.5 + x = -1.688194302 Solving 0.5 + x = -1.688194302 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 = -1.688194302 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.688194302 + -0.5 x = -1.688194302 + -0.5 Combine like terms: -1.688194302 + -0.5 = -2.188194302 x = -2.188194302 Simplifying x = -2.188194302Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.188194302, -2.188194302}Solution
x = {1.188194302, -2.188194302}
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