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Simplifying 48 = 15 + 6(4 + x) * 3x Reorder the terms for easier multiplication: 48 = 15 + 6 * 3x(4 + x) Multiply 6 * 3 48 = 15 + 18x(4 + x) 48 = 15 + (4 * 18x + x * 18x) 48 = 15 + (72x + 18x2) Solving 48 = 15 + 72x + 18x2 Solving for variable 'x'. Combine like terms: 48 + -15 = 33 33 + -72x + -18x2 = 15 + 72x + 18x2 + -15 + -72x + -18x2 Reorder the terms: 33 + -72x + -18x2 = 15 + -15 + 72x + -72x + 18x2 + -18x2 Combine like terms: 15 + -15 = 0 33 + -72x + -18x2 = 0 + 72x + -72x + 18x2 + -18x2 33 + -72x + -18x2 = 72x + -72x + 18x2 + -18x2 Combine like terms: 72x + -72x = 0 33 + -72x + -18x2 = 0 + 18x2 + -18x2 33 + -72x + -18x2 = 18x2 + -18x2 Combine like terms: 18x2 + -18x2 = 0 33 + -72x + -18x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(11 + -24x + -6x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(11 + -24x + -6x2)' equal to zero and attempt to solve: Simplifying 11 + -24x + -6x2 = 0 Solving 11 + -24x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -1.833333333 + 4x + x2 = 0 Move the constant term to the right: Add '1.833333333' to each side of the equation. -1.833333333 + 4x + 1.833333333 + x2 = 0 + 1.833333333 Reorder the terms: -1.833333333 + 1.833333333 + 4x + x2 = 0 + 1.833333333 Combine like terms: -1.833333333 + 1.833333333 = 0.000000000 0.000000000 + 4x + x2 = 0 + 1.833333333 4x + x2 = 0 + 1.833333333 Combine like terms: 0 + 1.833333333 = 1.833333333 4x + x2 = 1.833333333 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 = 1.833333333 + 4 Reorder the terms: 4 + 4x + x2 = 1.833333333 + 4 Combine like terms: 1.833333333 + 4 = 5.833333333 4 + 4x + x2 = 5.833333333 Factor a perfect square on the left side: (x + 2)(x + 2) = 5.833333333 Calculate the square root of the right side: 2.415229458 Break this problem into two subproblems by setting (x + 2) equal to 2.415229458 and -2.415229458.Subproblem 1
x + 2 = 2.415229458 Simplifying x + 2 = 2.415229458 Reorder the terms: 2 + x = 2.415229458 Solving 2 + x = 2.415229458 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 = 2.415229458 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.415229458 + -2 x = 2.415229458 + -2 Combine like terms: 2.415229458 + -2 = 0.415229458 x = 0.415229458 Simplifying x = 0.415229458Subproblem 2
x + 2 = -2.415229458 Simplifying x + 2 = -2.415229458 Reorder the terms: 2 + x = -2.415229458 Solving 2 + x = -2.415229458 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 = -2.415229458 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.415229458 + -2 x = -2.415229458 + -2 Combine like terms: -2.415229458 + -2 = -4.415229458 x = -4.415229458 Simplifying x = -4.415229458Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.415229458, -4.415229458}Solution
x = {0.415229458, -4.415229458}
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