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Simplifying 6x2 + 66x + -702 = 0 Reorder the terms: -702 + 66x + 6x2 = 0 Solving -702 + 66x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-117 + 11x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-117 + 11x + x2)' equal to zero and attempt to solve: Simplifying -117 + 11x + x2 = 0 Solving -117 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '117' to each side of the equation. -117 + 11x + 117 + x2 = 0 + 117 Reorder the terms: -117 + 117 + 11x + x2 = 0 + 117 Combine like terms: -117 + 117 = 0 0 + 11x + x2 = 0 + 117 11x + x2 = 0 + 117 Combine like terms: 0 + 117 = 117 11x + x2 = 117 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 117 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 117 + 30.25 Combine like terms: 117 + 30.25 = 147.25 30.25 + 11x + x2 = 147.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 147.25 Calculate the square root of the right side: 12.1346611 Break this problem into two subproblems by setting (x + 5.5) equal to 12.1346611 and -12.1346611.Subproblem 1
x + 5.5 = 12.1346611 Simplifying x + 5.5 = 12.1346611 Reorder the terms: 5.5 + x = 12.1346611 Solving 5.5 + x = 12.1346611 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 12.1346611 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 12.1346611 + -5.5 x = 12.1346611 + -5.5 Combine like terms: 12.1346611 + -5.5 = 6.6346611 x = 6.6346611 Simplifying x = 6.6346611Subproblem 2
x + 5.5 = -12.1346611 Simplifying x + 5.5 = -12.1346611 Reorder the terms: 5.5 + x = -12.1346611 Solving 5.5 + x = -12.1346611 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -12.1346611 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -12.1346611 + -5.5 x = -12.1346611 + -5.5 Combine like terms: -12.1346611 + -5.5 = -17.6346611 x = -17.6346611 Simplifying x = -17.6346611Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.6346611, -17.6346611}Solution
x = {6.6346611, -17.6346611}
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