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Simplifying 3x(2 + x) = 126 (2 * 3x + x * 3x) = 126 (6x + 3x2) = 126 Solving 6x + 3x2 = 126 Solving for variable 'x'. Reorder the terms: -126 + 6x + 3x2 = 126 + -126 Combine like terms: 126 + -126 = 0 -126 + 6x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-42 + 2x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-42 + 2x + x2)' equal to zero and attempt to solve: Simplifying -42 + 2x + x2 = 0 Solving -42 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + 2x + 42 + x2 = 0 + 42 Reorder the terms: -42 + 42 + 2x + x2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + 2x + x2 = 0 + 42 2x + x2 = 0 + 42 Combine like terms: 0 + 42 = 42 2x + x2 = 42 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 42 + 1 Reorder the terms: 1 + 2x + x2 = 42 + 1 Combine like terms: 42 + 1 = 43 1 + 2x + x2 = 43 Factor a perfect square on the left side: (x + 1)(x + 1) = 43 Calculate the square root of the right side: 6.557438524 Break this problem into two subproblems by setting (x + 1) equal to 6.557438524 and -6.557438524.Subproblem 1
x + 1 = 6.557438524 Simplifying x + 1 = 6.557438524 Reorder the terms: 1 + x = 6.557438524 Solving 1 + x = 6.557438524 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 6.557438524 + -1 Combine like terms: 1 + -1 = 0 0 + x = 6.557438524 + -1 x = 6.557438524 + -1 Combine like terms: 6.557438524 + -1 = 5.557438524 x = 5.557438524 Simplifying x = 5.557438524Subproblem 2
x + 1 = -6.557438524 Simplifying x + 1 = -6.557438524 Reorder the terms: 1 + x = -6.557438524 Solving 1 + x = -6.557438524 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -6.557438524 + -1 Combine like terms: 1 + -1 = 0 0 + x = -6.557438524 + -1 x = -6.557438524 + -1 Combine like terms: -6.557438524 + -1 = -7.557438524 x = -7.557438524 Simplifying x = -7.557438524Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.557438524, -7.557438524}Solution
x = {5.557438524, -7.557438524}
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