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Simplifying 5x(2x + 8) + -5x = (5x + 6) Reorder the terms: 5x(8 + 2x) + -5x = (5x + 6) (8 * 5x + 2x * 5x) + -5x = (5x + 6) (40x + 10x2) + -5x = (5x + 6) Reorder the terms: 40x + -5x + 10x2 = (5x + 6) Combine like terms: 40x + -5x = 35x 35x + 10x2 = (5x + 6) Reorder the terms: 35x + 10x2 = (6 + 5x) Remove parenthesis around (6 + 5x) 35x + 10x2 = 6 + 5x Solving 35x + 10x2 = 6 + 5x Solving for variable 'x'. Reorder the terms: -6 + 35x + -5x + 10x2 = 6 + 5x + -6 + -5x Combine like terms: 35x + -5x = 30x -6 + 30x + 10x2 = 6 + 5x + -6 + -5x Reorder the terms: -6 + 30x + 10x2 = 6 + -6 + 5x + -5x Combine like terms: 6 + -6 = 0 -6 + 30x + 10x2 = 0 + 5x + -5x -6 + 30x + 10x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -6 + 30x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 15x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 15x + 5x2)' equal to zero and attempt to solve: Simplifying -3 + 15x + 5x2 = 0 Solving -3 + 15x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.6 + 3x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + 3x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + 3x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + 3x + x2 = 0 + 0.6 3x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 3x + x2 = 0.6 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 0.6 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 0.6 + 2.25 Combine like terms: 0.6 + 2.25 = 2.85 2.25 + 3x + x2 = 2.85 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 2.85 Calculate the square root of the right side: 1.688194302 Break this problem into two subproblems by setting (x + 1.5) equal to 1.688194302 and -1.688194302.Subproblem 1
x + 1.5 = 1.688194302 Simplifying x + 1.5 = 1.688194302 Reorder the terms: 1.5 + x = 1.688194302 Solving 1.5 + x = 1.688194302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 1.688194302 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.688194302 + -1.5 x = 1.688194302 + -1.5 Combine like terms: 1.688194302 + -1.5 = 0.188194302 x = 0.188194302 Simplifying x = 0.188194302Subproblem 2
x + 1.5 = -1.688194302 Simplifying x + 1.5 = -1.688194302 Reorder the terms: 1.5 + x = -1.688194302 Solving 1.5 + x = -1.688194302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -1.688194302 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.688194302 + -1.5 x = -1.688194302 + -1.5 Combine like terms: -1.688194302 + -1.5 = -3.188194302 x = -3.188194302 Simplifying x = -3.188194302Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.188194302, -3.188194302}Solution
x = {0.188194302, -3.188194302}
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