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Simplifying 0 = 6x2 + 6x + -378 Reorder the terms: 0 = -378 + 6x + 6x2 Solving 0 = -378 + 6x + 6x2 Solving for variable 'x'. Combine like terms: 0 + 378 = 378 378 + -6x + -6x2 = -378 + 6x + 6x2 + 378 + -6x + -6x2 Reorder the terms: 378 + -6x + -6x2 = -378 + 378 + 6x + -6x + 6x2 + -6x2 Combine like terms: -378 + 378 = 0 378 + -6x + -6x2 = 0 + 6x + -6x + 6x2 + -6x2 378 + -6x + -6x2 = 6x + -6x + 6x2 + -6x2 Combine like terms: 6x + -6x = 0 378 + -6x + -6x2 = 0 + 6x2 + -6x2 378 + -6x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 378 + -6x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(63 + -1x + -1x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(63 + -1x + -1x2)' equal to zero and attempt to solve: Simplifying 63 + -1x + -1x2 = 0 Solving 63 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -63 + x + x2 = 0 Move the constant term to the right: Add '63' to each side of the equation. -63 + x + 63 + x2 = 0 + 63 Reorder the terms: -63 + 63 + x + x2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + x + x2 = 0 + 63 x + x2 = 0 + 63 Combine like terms: 0 + 63 = 63 x + x2 = 63 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. + 0.25 + x2 = 63 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 63 + 0.25 Combine like terms: 63 + 0.25 = 63.25 1.25 + x2 = 63.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 63.25 Calculate the square root of the right side: 7.95298686 Break this problem into two subproblems by setting (x + 0.5) equal to 7.95298686 and -7.95298686.Subproblem 1
x + 0.5 = 7.95298686 Simplifying x + 0.5 = 7.95298686 Reorder the terms: 0.5 + x = 7.95298686 Solving 0.5 + x = 7.95298686 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 = 7.95298686 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 7.95298686 + -0.5 x = 7.95298686 + -0.5 Combine like terms: 7.95298686 + -0.5 = 7.45298686 x = 7.45298686 Simplifying x = 7.45298686Subproblem 2
x + 0.5 = -7.95298686 Simplifying x + 0.5 = -7.95298686 Reorder the terms: 0.5 + x = -7.95298686 Solving 0.5 + x = -7.95298686 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 = -7.95298686 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -7.95298686 + -0.5 x = -7.95298686 + -0.5 Combine like terms: -7.95298686 + -0.5 = -8.45298686 x = -8.45298686 Simplifying x = -8.45298686Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.45298686, -8.45298686}Solution
x = {7.45298686, -8.45298686}
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