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Simplifying 6x(x + 4) = 75 Reorder the terms: 6x(4 + x) = 75 (4 * 6x + x * 6x) = 75 (24x + 6x2) = 75 Solving 24x + 6x2 = 75 Solving for variable 'x'. Reorder the terms: -75 + 24x + 6x2 = 75 + -75 Combine like terms: 75 + -75 = 0 -75 + 24x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-25 + 8x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-25 + 8x + 2x2)' equal to zero and attempt to solve: Simplifying -25 + 8x + 2x2 = 0 Solving -25 + 8x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12.5 + 4x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + 4x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + 4x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + 4x + x2 = 0 + 12.5 4x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 4x + x2 = 12.5 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 12.5 + 4 Reorder the terms: 4 + 4x + x2 = 12.5 + 4 Combine like terms: 12.5 + 4 = 16.5 4 + 4x + x2 = 16.5 Factor a perfect square on the left side: (x + 2)(x + 2) = 16.5 Calculate the square root of the right side: 4.062019202 Break this problem into two subproblems by setting (x + 2) equal to 4.062019202 and -4.062019202.Subproblem 1
x + 2 = 4.062019202 Simplifying x + 2 = 4.062019202 Reorder the terms: 2 + x = 4.062019202 Solving 2 + x = 4.062019202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 4.062019202 + -2 Combine like terms: 2 + -2 = 0 0 + x = 4.062019202 + -2 x = 4.062019202 + -2 Combine like terms: 4.062019202 + -2 = 2.062019202 x = 2.062019202 Simplifying x = 2.062019202Subproblem 2
x + 2 = -4.062019202 Simplifying x + 2 = -4.062019202 Reorder the terms: 2 + x = -4.062019202 Solving 2 + x = -4.062019202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -4.062019202 + -2 Combine like terms: 2 + -2 = 0 0 + x = -4.062019202 + -2 x = -4.062019202 + -2 Combine like terms: -4.062019202 + -2 = -6.062019202 x = -6.062019202 Simplifying x = -6.062019202Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.062019202, -6.062019202}Solution
x = {2.062019202, -6.062019202}
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