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Simplifying 5 + 5(3x + 5) = 8x(3x + -18) Reorder the terms: 5 + 5(5 + 3x) = 8x(3x + -18) 5 + (5 * 5 + 3x * 5) = 8x(3x + -18) 5 + (25 + 15x) = 8x(3x + -18) Combine like terms: 5 + 25 = 30 30 + 15x = 8x(3x + -18) Reorder the terms: 30 + 15x = 8x(-18 + 3x) 30 + 15x = (-18 * 8x + 3x * 8x) 30 + 15x = (-144x + 24x2) Solving 30 + 15x = -144x + 24x2 Solving for variable 'x'. Combine like terms: 15x + 144x = 159x 30 + 159x + -24x2 = -144x + 24x2 + 144x + -24x2 Reorder the terms: 30 + 159x + -24x2 = -144x + 144x + 24x2 + -24x2 Combine like terms: -144x + 144x = 0 30 + 159x + -24x2 = 0 + 24x2 + -24x2 30 + 159x + -24x2 = 24x2 + -24x2 Combine like terms: 24x2 + -24x2 = 0 30 + 159x + -24x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(10 + 53x + -8x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(10 + 53x + -8x2)' equal to zero and attempt to solve: Simplifying 10 + 53x + -8x2 = 0 Solving 10 + 53x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -1.25 + -6.625x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -6.625x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -6.625x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -6.625x + x2 = 0 + 1.25 -6.625x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -6.625x + x2 = 1.25 The x term is -6.625x. Take half its coefficient (-3.3125). Square it (10.97265625) and add it to both sides. Add '10.97265625' to each side of the equation. -6.625x + 10.97265625 + x2 = 1.25 + 10.97265625 Reorder the terms: 10.97265625 + -6.625x + x2 = 1.25 + 10.97265625 Combine like terms: 1.25 + 10.97265625 = 12.22265625 10.97265625 + -6.625x + x2 = 12.22265625 Factor a perfect square on the left side: (x + -3.3125)(x + -3.3125) = 12.22265625 Calculate the square root of the right side: 3.496091568 Break this problem into two subproblems by setting (x + -3.3125) equal to 3.496091568 and -3.496091568.Subproblem 1
x + -3.3125 = 3.496091568 Simplifying x + -3.3125 = 3.496091568 Reorder the terms: -3.3125 + x = 3.496091568 Solving -3.3125 + x = 3.496091568 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.3125' to each side of the equation. -3.3125 + 3.3125 + x = 3.496091568 + 3.3125 Combine like terms: -3.3125 + 3.3125 = 0.0000 0.0000 + x = 3.496091568 + 3.3125 x = 3.496091568 + 3.3125 Combine like terms: 3.496091568 + 3.3125 = 6.808591568 x = 6.808591568 Simplifying x = 6.808591568Subproblem 2
x + -3.3125 = -3.496091568 Simplifying x + -3.3125 = -3.496091568 Reorder the terms: -3.3125 + x = -3.496091568 Solving -3.3125 + x = -3.496091568 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.3125' to each side of the equation. -3.3125 + 3.3125 + x = -3.496091568 + 3.3125 Combine like terms: -3.3125 + 3.3125 = 0.0000 0.0000 + x = -3.496091568 + 3.3125 x = -3.496091568 + 3.3125 Combine like terms: -3.496091568 + 3.3125 = -0.183591568 x = -0.183591568 Simplifying x = -0.183591568Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.808591568, -0.183591568}Solution
x = {6.808591568, -0.183591568}
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