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Simplifying (4x2 + -6x + -68) + (6x2 + 8x) = 0 Reorder the terms: (-68 + -6x + 4x2) + (6x2 + 8x) = 0 Remove parenthesis around (-68 + -6x + 4x2) -68 + -6x + 4x2 + (6x2 + 8x) = 0 Reorder the terms: -68 + -6x + 4x2 + (8x + 6x2) = 0 Remove parenthesis around (8x + 6x2) -68 + -6x + 4x2 + 8x + 6x2 = 0 Reorder the terms: -68 + -6x + 8x + 4x2 + 6x2 = 0 Combine like terms: -6x + 8x = 2x -68 + 2x + 4x2 + 6x2 = 0 Combine like terms: 4x2 + 6x2 = 10x2 -68 + 2x + 10x2 = 0 Solving -68 + 2x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-34 + x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-34 + x + 5x2)' equal to zero and attempt to solve: Simplifying -34 + x + 5x2 = 0 Solving -34 + x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -6.8 + 0.2x + x2 = 0 Move the constant term to the right: Add '6.8' to each side of the equation. -6.8 + 0.2x + 6.8 + x2 = 0 + 6.8 Reorder the terms: -6.8 + 6.8 + 0.2x + x2 = 0 + 6.8 Combine like terms: -6.8 + 6.8 = 0.0 0.0 + 0.2x + x2 = 0 + 6.8 0.2x + x2 = 0 + 6.8 Combine like terms: 0 + 6.8 = 6.8 0.2x + x2 = 6.8 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 = 6.8 + 0.25 Reorder the terms: 0.25 + 0.2x + x2 = 6.8 + 0.25 Combine like terms: 6.8 + 0.25 = 7.05 0.25 + 0.2x + x2 = 7.05 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 7.05 Calculate the square root of the right side: 2.655183609 Break this problem into two subproblems by setting (x + 0.5) equal to 2.655183609 and -2.655183609.Subproblem 1
x + 0.5 = 2.655183609 Simplifying x + 0.5 = 2.655183609 Reorder the terms: 0.5 + x = 2.655183609 Solving 0.5 + x = 2.655183609 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 = 2.655183609 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.655183609 + -0.5 x = 2.655183609 + -0.5 Combine like terms: 2.655183609 + -0.5 = 2.155183609 x = 2.155183609 Simplifying x = 2.155183609Subproblem 2
x + 0.5 = -2.655183609 Simplifying x + 0.5 = -2.655183609 Reorder the terms: 0.5 + x = -2.655183609 Solving 0.5 + x = -2.655183609 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 = -2.655183609 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.655183609 + -0.5 x = -2.655183609 + -0.5 Combine like terms: -2.655183609 + -0.5 = -3.155183609 x = -3.155183609 Simplifying x = -3.155183609Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.155183609, -3.155183609}Solution
x = {2.155183609, -3.155183609}
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