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Simplifying 6x2 + 12x = 963 Reorder the terms: 12x + 6x2 = 963 Solving 12x + 6x2 = 963 Solving for variable 'x'. Reorder the terms: -963 + 12x + 6x2 = 963 + -963 Combine like terms: 963 + -963 = 0 -963 + 12x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-321 + 4x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-321 + 4x + 2x2)' equal to zero and attempt to solve: Simplifying -321 + 4x + 2x2 = 0 Solving -321 + 4x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -160.5 + 2x + x2 = 0 Move the constant term to the right: Add '160.5' to each side of the equation. -160.5 + 2x + 160.5 + x2 = 0 + 160.5 Reorder the terms: -160.5 + 160.5 + 2x + x2 = 0 + 160.5 Combine like terms: -160.5 + 160.5 = 0.0 0.0 + 2x + x2 = 0 + 160.5 2x + x2 = 0 + 160.5 Combine like terms: 0 + 160.5 = 160.5 2x + x2 = 160.5 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 = 160.5 + 1 Reorder the terms: 1 + 2x + x2 = 160.5 + 1 Combine like terms: 160.5 + 1 = 161.5 1 + 2x + x2 = 161.5 Factor a perfect square on the left side: (x + 1)(x + 1) = 161.5 Calculate the square root of the right side: 12.708265027 Break this problem into two subproblems by setting (x + 1) equal to 12.708265027 and -12.708265027.Subproblem 1
x + 1 = 12.708265027 Simplifying x + 1 = 12.708265027 Reorder the terms: 1 + x = 12.708265027 Solving 1 + x = 12.708265027 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 = 12.708265027 + -1 Combine like terms: 1 + -1 = 0 0 + x = 12.708265027 + -1 x = 12.708265027 + -1 Combine like terms: 12.708265027 + -1 = 11.708265027 x = 11.708265027 Simplifying x = 11.708265027Subproblem 2
x + 1 = -12.708265027 Simplifying x + 1 = -12.708265027 Reorder the terms: 1 + x = -12.708265027 Solving 1 + x = -12.708265027 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 = -12.708265027 + -1 Combine like terms: 1 + -1 = 0 0 + x = -12.708265027 + -1 x = -12.708265027 + -1 Combine like terms: -12.708265027 + -1 = -13.708265027 x = -13.708265027 Simplifying x = -13.708265027Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.708265027, -13.708265027}Solution
x = {11.708265027, -13.708265027}
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