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Simplifying 2x(4 + x) = 78 (4 * 2x + x * 2x) = 78 (8x + 2x2) = 78 Solving 8x + 2x2 = 78 Solving for variable 'x'. Reorder the terms: -78 + 8x + 2x2 = 78 + -78 Combine like terms: 78 + -78 = 0 -78 + 8x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-39 + 4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-39 + 4x + x2)' equal to zero and attempt to solve: Simplifying -39 + 4x + x2 = 0 Solving -39 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '39' to each side of the equation. -39 + 4x + 39 + x2 = 0 + 39 Reorder the terms: -39 + 39 + 4x + x2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + 4x + x2 = 0 + 39 4x + x2 = 0 + 39 Combine like terms: 0 + 39 = 39 4x + x2 = 39 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 = 39 + 4 Reorder the terms: 4 + 4x + x2 = 39 + 4 Combine like terms: 39 + 4 = 43 4 + 4x + x2 = 43 Factor a perfect square on the left side: (x + 2)(x + 2) = 43 Calculate the square root of the right side: 6.557438524 Break this problem into two subproblems by setting (x + 2) equal to 6.557438524 and -6.557438524.Subproblem 1
x + 2 = 6.557438524 Simplifying x + 2 = 6.557438524 Reorder the terms: 2 + x = 6.557438524 Solving 2 + x = 6.557438524 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 = 6.557438524 + -2 Combine like terms: 2 + -2 = 0 0 + x = 6.557438524 + -2 x = 6.557438524 + -2 Combine like terms: 6.557438524 + -2 = 4.557438524 x = 4.557438524 Simplifying x = 4.557438524Subproblem 2
x + 2 = -6.557438524 Simplifying x + 2 = -6.557438524 Reorder the terms: 2 + x = -6.557438524 Solving 2 + x = -6.557438524 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 = -6.557438524 + -2 Combine like terms: 2 + -2 = 0 0 + x = -6.557438524 + -2 x = -6.557438524 + -2 Combine like terms: -6.557438524 + -2 = -8.557438524 x = -8.557438524 Simplifying x = -8.557438524Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.557438524, -8.557438524}Solution
x = {4.557438524, -8.557438524}
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