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Simplifying 2x2 + 6x + -94 = 0 Reorder the terms: -94 + 6x + 2x2 = 0 Solving -94 + 6x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-47 + 3x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-47 + 3x + x2)' equal to zero and attempt to solve: Simplifying -47 + 3x + x2 = 0 Solving -47 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + 3x + 47 + x2 = 0 + 47 Reorder the terms: -47 + 47 + 3x + x2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + 3x + x2 = 0 + 47 3x + x2 = 0 + 47 Combine like terms: 0 + 47 = 47 3x + x2 = 47 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 47 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 47 + 2.25 Combine like terms: 47 + 2.25 = 49.25 2.25 + 3x + x2 = 49.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 49.25 Calculate the square root of the right side: 7.017834424 Break this problem into two subproblems by setting (x + 1.5) equal to 7.017834424 and -7.017834424.Subproblem 1
x + 1.5 = 7.017834424 Simplifying x + 1.5 = 7.017834424 Reorder the terms: 1.5 + x = 7.017834424 Solving 1.5 + x = 7.017834424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 7.017834424 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 7.017834424 + -1.5 x = 7.017834424 + -1.5 Combine like terms: 7.017834424 + -1.5 = 5.517834424 x = 5.517834424 Simplifying x = 5.517834424Subproblem 2
x + 1.5 = -7.017834424 Simplifying x + 1.5 = -7.017834424 Reorder the terms: 1.5 + x = -7.017834424 Solving 1.5 + x = -7.017834424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -7.017834424 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -7.017834424 + -1.5 x = -7.017834424 + -1.5 Combine like terms: -7.017834424 + -1.5 = -8.517834424 x = -8.517834424 Simplifying x = -8.517834424Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.517834424, -8.517834424}Solution
x = {5.517834424, -8.517834424}
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