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Simplifying 6x2 + 6x + -366 = 0 Reorder the terms: -366 + 6x + 6x2 = 0 Solving -366 + 6x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-61 + x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-61 + x + x2)' equal to zero and attempt to solve: Simplifying -61 + x + x2 = 0 Solving -61 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '61' to each side of the equation. -61 + x + 61 + x2 = 0 + 61 Reorder the terms: -61 + 61 + x + x2 = 0 + 61 Combine like terms: -61 + 61 = 0 0 + x + x2 = 0 + 61 x + x2 = 0 + 61 Combine like terms: 0 + 61 = 61 x + x2 = 61 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 61 + 0.25 Reorder the terms: 0.25 + x + x2 = 61 + 0.25 Combine like terms: 61 + 0.25 = 61.25 0.25 + x + x2 = 61.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 61.25 Calculate the square root of the right side: 7.826237921 Break this problem into two subproblems by setting (x + 0.5) equal to 7.826237921 and -7.826237921.Subproblem 1
x + 0.5 = 7.826237921 Simplifying x + 0.5 = 7.826237921 Reorder the terms: 0.5 + x = 7.826237921 Solving 0.5 + x = 7.826237921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 7.826237921 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 7.826237921 + -0.5 x = 7.826237921 + -0.5 Combine like terms: 7.826237921 + -0.5 = 7.326237921 x = 7.326237921 Simplifying x = 7.326237921Subproblem 2
x + 0.5 = -7.826237921 Simplifying x + 0.5 = -7.826237921 Reorder the terms: 0.5 + x = -7.826237921 Solving 0.5 + x = -7.826237921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -7.826237921 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -7.826237921 + -0.5 x = -7.826237921 + -0.5 Combine like terms: -7.826237921 + -0.5 = -8.326237921 x = -8.326237921 Simplifying x = -8.326237921Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.326237921, -8.326237921}Solution
x = {7.326237921, -8.326237921}
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