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Simplifying 26x(x + 4) = 4800 Reorder the terms: 26x(4 + x) = 4800 (4 * 26x + x * 26x) = 4800 (104x + 26x2) = 4800 Solving 104x + 26x2 = 4800 Solving for variable 'x'. Reorder the terms: -4800 + 104x + 26x2 = 4800 + -4800 Combine like terms: 4800 + -4800 = 0 -4800 + 104x + 26x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2400 + 52x + 13x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2400 + 52x + 13x2)' equal to zero and attempt to solve: Simplifying -2400 + 52x + 13x2 = 0 Solving -2400 + 52x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -184.6153846 + 4x + x2 = 0 Move the constant term to the right: Add '184.6153846' to each side of the equation. -184.6153846 + 4x + 184.6153846 + x2 = 0 + 184.6153846 Reorder the terms: -184.6153846 + 184.6153846 + 4x + x2 = 0 + 184.6153846 Combine like terms: -184.6153846 + 184.6153846 = 0.0000000 0.0000000 + 4x + x2 = 0 + 184.6153846 4x + x2 = 0 + 184.6153846 Combine like terms: 0 + 184.6153846 = 184.6153846 4x + x2 = 184.6153846 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 = 184.6153846 + 4 Reorder the terms: 4 + 4x + x2 = 184.6153846 + 4 Combine like terms: 184.6153846 + 4 = 188.6153846 4 + 4x + x2 = 188.6153846 Factor a perfect square on the left side: (x + 2)(x + 2) = 188.6153846 Calculate the square root of the right side: 13.733731634 Break this problem into two subproblems by setting (x + 2) equal to 13.733731634 and -13.733731634.Subproblem 1
x + 2 = 13.733731634 Simplifying x + 2 = 13.733731634 Reorder the terms: 2 + x = 13.733731634 Solving 2 + x = 13.733731634 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 = 13.733731634 + -2 Combine like terms: 2 + -2 = 0 0 + x = 13.733731634 + -2 x = 13.733731634 + -2 Combine like terms: 13.733731634 + -2 = 11.733731634 x = 11.733731634 Simplifying x = 11.733731634Subproblem 2
x + 2 = -13.733731634 Simplifying x + 2 = -13.733731634 Reorder the terms: 2 + x = -13.733731634 Solving 2 + x = -13.733731634 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 = -13.733731634 + -2 Combine like terms: 2 + -2 = 0 0 + x = -13.733731634 + -2 x = -13.733731634 + -2 Combine like terms: -13.733731634 + -2 = -15.733731634 x = -15.733731634 Simplifying x = -15.733731634Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.733731634, -15.733731634}Solution
x = {11.733731634, -15.733731634}
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