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Simplifying 6x2 + 8x + -780 = 0 Reorder the terms: -780 + 8x + 6x2 = 0 Solving -780 + 8x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-390 + 4x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-390 + 4x + 3x2)' equal to zero and attempt to solve: Simplifying -390 + 4x + 3x2 = 0 Solving -390 + 4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -130 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '130' to each side of the equation. -130 + 1.333333333x + 130 + x2 = 0 + 130 Reorder the terms: -130 + 130 + 1.333333333x + x2 = 0 + 130 Combine like terms: -130 + 130 = 0 0 + 1.333333333x + x2 = 0 + 130 1.333333333x + x2 = 0 + 130 Combine like terms: 0 + 130 = 130 1.333333333x + x2 = 130 The x term is 1.333333333x. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333x + 0.4444444442 + x2 = 130 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 130 + 0.4444444442 Combine like terms: 130 + 0.4444444442 = 130.4444444442 0.4444444442 + 1.333333333x + x2 = 130.4444444442 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 130.4444444442 Calculate the square root of the right side: 11.421227799 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 11.421227799 and -11.421227799.Subproblem 1
x + 0.6666666665 = 11.421227799 Simplifying x + 0.6666666665 = 11.421227799 Reorder the terms: 0.6666666665 + x = 11.421227799 Solving 0.6666666665 + x = 11.421227799 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = 11.421227799 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 11.421227799 + -0.6666666665 x = 11.421227799 + -0.6666666665 Combine like terms: 11.421227799 + -0.6666666665 = 10.7545611325 x = 10.7545611325 Simplifying x = 10.7545611325Subproblem 2
x + 0.6666666665 = -11.421227799 Simplifying x + 0.6666666665 = -11.421227799 Reorder the terms: 0.6666666665 + x = -11.421227799 Solving 0.6666666665 + x = -11.421227799 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = -11.421227799 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -11.421227799 + -0.6666666665 x = -11.421227799 + -0.6666666665 Combine like terms: -11.421227799 + -0.6666666665 = -12.0878944655 x = -12.0878944655 Simplifying x = -12.0878944655Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.7545611325, -12.0878944655}Solution
x = {10.7545611325, -12.0878944655}
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