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Simplifying (2x) * x + (12) * x + -780 = 0 Remove parenthesis around (2x) 2x * x + (12) * x + -780 = 0 Multiply x * x 2x2 + (12) * x + -780 = 0 Reorder the terms: -780 + 12x + 2x2 = 0 Solving -780 + 12x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-390 + 6x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-390 + 6x + x2)' equal to zero and attempt to solve: Simplifying -390 + 6x + x2 = 0 Solving -390 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '390' to each side of the equation. -390 + 6x + 390 + x2 = 0 + 390 Reorder the terms: -390 + 390 + 6x + x2 = 0 + 390 Combine like terms: -390 + 390 = 0 0 + 6x + x2 = 0 + 390 6x + x2 = 0 + 390 Combine like terms: 0 + 390 = 390 6x + x2 = 390 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 = 390 + 9 Reorder the terms: 9 + 6x + x2 = 390 + 9 Combine like terms: 390 + 9 = 399 9 + 6x + x2 = 399 Factor a perfect square on the left side: (x + 3)(x + 3) = 399 Calculate the square root of the right side: 19.974984355 Break this problem into two subproblems by setting (x + 3) equal to 19.974984355 and -19.974984355.Subproblem 1
x + 3 = 19.974984355 Simplifying x + 3 = 19.974984355 Reorder the terms: 3 + x = 19.974984355 Solving 3 + x = 19.974984355 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 = 19.974984355 + -3 Combine like terms: 3 + -3 = 0 0 + x = 19.974984355 + -3 x = 19.974984355 + -3 Combine like terms: 19.974984355 + -3 = 16.974984355 x = 16.974984355 Simplifying x = 16.974984355Subproblem 2
x + 3 = -19.974984355 Simplifying x + 3 = -19.974984355 Reorder the terms: 3 + x = -19.974984355 Solving 3 + x = -19.974984355 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 = -19.974984355 + -3 Combine like terms: 3 + -3 = 0 0 + x = -19.974984355 + -3 x = -19.974984355 + -3 Combine like terms: -19.974984355 + -3 = -22.974984355 x = -22.974984355 Simplifying x = -22.974984355Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.974984355, -22.974984355}Solution
x = {16.974984355, -22.974984355}
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