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Simplifying 2x(13 + 4x) = 6x + -2(8x + -3) (13 * 2x + 4x * 2x) = 6x + -2(8x + -3) (26x + 8x2) = 6x + -2(8x + -3) Reorder the terms: 26x + 8x2 = 6x + -2(-3 + 8x) 26x + 8x2 = 6x + (-3 * -2 + 8x * -2) 26x + 8x2 = 6x + (6 + -16x) Reorder the terms: 26x + 8x2 = 6 + 6x + -16x Combine like terms: 6x + -16x = -10x 26x + 8x2 = 6 + -10x Solving 26x + 8x2 = 6 + -10x Solving for variable 'x'. Reorder the terms: -6 + 26x + 10x + 8x2 = 6 + -10x + -6 + 10x Combine like terms: 26x + 10x = 36x -6 + 36x + 8x2 = 6 + -10x + -6 + 10x Reorder the terms: -6 + 36x + 8x2 = 6 + -6 + -10x + 10x Combine like terms: 6 + -6 = 0 -6 + 36x + 8x2 = 0 + -10x + 10x -6 + 36x + 8x2 = -10x + 10x Combine like terms: -10x + 10x = 0 -6 + 36x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 18x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 18x + 4x2)' equal to zero and attempt to solve: Simplifying -3 + 18x + 4x2 = 0 Solving -3 + 18x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + 4.5x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 4.5x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 4.5x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 4.5x + x2 = 0 + 0.75 4.5x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 4.5x + x2 = 0.75 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 0.75 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 0.75 + 5.0625 Combine like terms: 0.75 + 5.0625 = 5.8125 5.0625 + 4.5x + x2 = 5.8125 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 5.8125 Calculate the square root of the right side: 2.41091269 Break this problem into two subproblems by setting (x + 2.25) equal to 2.41091269 and -2.41091269.Subproblem 1
x + 2.25 = 2.41091269 Simplifying x + 2.25 = 2.41091269 Reorder the terms: 2.25 + x = 2.41091269 Solving 2.25 + x = 2.41091269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 2.41091269 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 2.41091269 + -2.25 x = 2.41091269 + -2.25 Combine like terms: 2.41091269 + -2.25 = 0.16091269 x = 0.16091269 Simplifying x = 0.16091269Subproblem 2
x + 2.25 = -2.41091269 Simplifying x + 2.25 = -2.41091269 Reorder the terms: 2.25 + x = -2.41091269 Solving 2.25 + x = -2.41091269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -2.41091269 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -2.41091269 + -2.25 x = -2.41091269 + -2.25 Combine like terms: -2.41091269 + -2.25 = -4.66091269 x = -4.66091269 Simplifying x = -4.66091269Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.16091269, -4.66091269}Solution
x = {0.16091269, -4.66091269}
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