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Simplifying 3 = 2x2 + 6x + -7 Reorder the terms: 3 = -7 + 6x + 2x2 Solving 3 = -7 + 6x + 2x2 Solving for variable 'x'. Combine like terms: 3 + 7 = 10 10 + -6x + -2x2 = -7 + 6x + 2x2 + 7 + -6x + -2x2 Reorder the terms: 10 + -6x + -2x2 = -7 + 7 + 6x + -6x + 2x2 + -2x2 Combine like terms: -7 + 7 = 0 10 + -6x + -2x2 = 0 + 6x + -6x + 2x2 + -2x2 10 + -6x + -2x2 = 6x + -6x + 2x2 + -2x2 Combine like terms: 6x + -6x = 0 10 + -6x + -2x2 = 0 + 2x2 + -2x2 10 + -6x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 10 + -6x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -3x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -3x + -1x2)' equal to zero and attempt to solve: Simplifying 5 + -3x + -1x2 = 0 Solving 5 + -3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + 3x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 3x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 3x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 3x + x2 = 0 + 5 3x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 3x + x2 = 5 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 = 5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 5 + 2.25 Combine like terms: 5 + 2.25 = 7.25 2.25 + 3x + x2 = 7.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (x + 1.5) equal to 2.692582404 and -2.692582404.Subproblem 1
x + 1.5 = 2.692582404 Simplifying x + 1.5 = 2.692582404 Reorder the terms: 1.5 + x = 2.692582404 Solving 1.5 + x = 2.692582404 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 = 2.692582404 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.692582404 + -1.5 x = 2.692582404 + -1.5 Combine like terms: 2.692582404 + -1.5 = 1.192582404 x = 1.192582404 Simplifying x = 1.192582404Subproblem 2
x + 1.5 = -2.692582404 Simplifying x + 1.5 = -2.692582404 Reorder the terms: 1.5 + x = -2.692582404 Solving 1.5 + x = -2.692582404 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 = -2.692582404 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.692582404 + -1.5 x = -2.692582404 + -1.5 Combine like terms: -2.692582404 + -1.5 = -4.192582404 x = -4.192582404 Simplifying x = -4.192582404Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.192582404, -4.192582404}Solution
x = {1.192582404, -4.192582404}
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