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Simplifying 4x2 + 24x + 336 = 540 Reorder the terms: 336 + 24x + 4x2 = 540 Solving 336 + 24x + 4x2 = 540 Solving for variable 'x'. Reorder the terms: 336 + -540 + 24x + 4x2 = 540 + -540 Combine like terms: 336 + -540 = -204 -204 + 24x + 4x2 = 540 + -540 Combine like terms: 540 + -540 = 0 -204 + 24x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-51 + 6x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-51 + 6x + x2)' equal to zero and attempt to solve: Simplifying -51 + 6x + x2 = 0 Solving -51 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '51' to each side of the equation. -51 + 6x + 51 + x2 = 0 + 51 Reorder the terms: -51 + 51 + 6x + x2 = 0 + 51 Combine like terms: -51 + 51 = 0 0 + 6x + x2 = 0 + 51 6x + x2 = 0 + 51 Combine like terms: 0 + 51 = 51 6x + x2 = 51 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 51 + 9 Reorder the terms: 9 + 6x + x2 = 51 + 9 Combine like terms: 51 + 9 = 60 9 + 6x + x2 = 60 Factor a perfect square on the left side: (x + 3)(x + 3) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (x + 3) equal to 7.745966692 and -7.745966692.Subproblem 1
x + 3 = 7.745966692 Simplifying x + 3 = 7.745966692 Reorder the terms: 3 + x = 7.745966692 Solving 3 + x = 7.745966692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 7.745966692 + -3 Combine like terms: 3 + -3 = 0 0 + x = 7.745966692 + -3 x = 7.745966692 + -3 Combine like terms: 7.745966692 + -3 = 4.745966692 x = 4.745966692 Simplifying x = 4.745966692Subproblem 2
x + 3 = -7.745966692 Simplifying x + 3 = -7.745966692 Reorder the terms: 3 + x = -7.745966692 Solving 3 + x = -7.745966692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -7.745966692 + -3 Combine like terms: 3 + -3 = 0 0 + x = -7.745966692 + -3 x = -7.745966692 + -3 Combine like terms: -7.745966692 + -3 = -10.745966692 x = -10.745966692 Simplifying x = -10.745966692Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.745966692, -10.745966692}Solution
x = {4.745966692, -10.745966692}
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