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Simplifying 8x(13x + 49) = 135(2) Reorder the terms: 8x(49 + 13x) = 135(2) (49 * 8x + 13x * 8x) = 135(2) (392x + 104x2) = 135(2) Multiply 135 * 2 392x + 104x2 = 270 Solving 392x + 104x2 = 270 Solving for variable 'x'. Reorder the terms: -270 + 392x + 104x2 = 270 + -270 Combine like terms: 270 + -270 = 0 -270 + 392x + 104x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-135 + 196x + 52x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-135 + 196x + 52x2)' equal to zero and attempt to solve: Simplifying -135 + 196x + 52x2 = 0 Solving -135 + 196x + 52x2 = 0 Begin completing the square. Divide all terms by 52 the coefficient of the squared term: Divide each side by '52'. -2.596153846 + 3.769230769x + x2 = 0 Move the constant term to the right: Add '2.596153846' to each side of the equation. -2.596153846 + 3.769230769x + 2.596153846 + x2 = 0 + 2.596153846 Reorder the terms: -2.596153846 + 2.596153846 + 3.769230769x + x2 = 0 + 2.596153846 Combine like terms: -2.596153846 + 2.596153846 = 0.000000000 0.000000000 + 3.769230769x + x2 = 0 + 2.596153846 3.769230769x + x2 = 0 + 2.596153846 Combine like terms: 0 + 2.596153846 = 2.596153846 3.769230769x + x2 = 2.596153846 The x term is 3.769230769x. Take half its coefficient (1.884615385). Square it (3.551775149) and add it to both sides. Add '3.551775149' to each side of the equation. 3.769230769x + 3.551775149 + x2 = 2.596153846 + 3.551775149 Reorder the terms: 3.551775149 + 3.769230769x + x2 = 2.596153846 + 3.551775149 Combine like terms: 2.596153846 + 3.551775149 = 6.147928995 3.551775149 + 3.769230769x + x2 = 6.147928995 Factor a perfect square on the left side: (x + 1.884615385)(x + 1.884615385) = 6.147928995 Calculate the square root of the right side: 2.479501763 Break this problem into two subproblems by setting (x + 1.884615385) equal to 2.479501763 and -2.479501763.Subproblem 1
x + 1.884615385 = 2.479501763 Simplifying x + 1.884615385 = 2.479501763 Reorder the terms: 1.884615385 + x = 2.479501763 Solving 1.884615385 + x = 2.479501763 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.884615385' to each side of the equation. 1.884615385 + -1.884615385 + x = 2.479501763 + -1.884615385 Combine like terms: 1.884615385 + -1.884615385 = 0.000000000 0.000000000 + x = 2.479501763 + -1.884615385 x = 2.479501763 + -1.884615385 Combine like terms: 2.479501763 + -1.884615385 = 0.594886378 x = 0.594886378 Simplifying x = 0.594886378Subproblem 2
x + 1.884615385 = -2.479501763 Simplifying x + 1.884615385 = -2.479501763 Reorder the terms: 1.884615385 + x = -2.479501763 Solving 1.884615385 + x = -2.479501763 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.884615385' to each side of the equation. 1.884615385 + -1.884615385 + x = -2.479501763 + -1.884615385 Combine like terms: 1.884615385 + -1.884615385 = 0.000000000 0.000000000 + x = -2.479501763 + -1.884615385 x = -2.479501763 + -1.884615385 Combine like terms: -2.479501763 + -1.884615385 = -4.364117148 x = -4.364117148 Simplifying x = -4.364117148Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.594886378, -4.364117148}Solution
x = {0.594886378, -4.364117148}
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