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Simplifying 2(x2 + 3x + -123) = 0 Reorder the terms: 2(-123 + 3x + x2) = 0 (-123 * 2 + 3x * 2 + x2 * 2) = 0 (-246 + 6x + 2x2) = 0 Solving -246 + 6x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-123 + 3x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-123 + 3x + x2)' equal to zero and attempt to solve: Simplifying -123 + 3x + x2 = 0 Solving -123 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '123' to each side of the equation. -123 + 3x + 123 + x2 = 0 + 123 Reorder the terms: -123 + 123 + 3x + x2 = 0 + 123 Combine like terms: -123 + 123 = 0 0 + 3x + x2 = 0 + 123 3x + x2 = 0 + 123 Combine like terms: 0 + 123 = 123 3x + x2 = 123 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 = 123 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 123 + 2.25 Combine like terms: 123 + 2.25 = 125.25 2.25 + 3x + x2 = 125.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 125.25 Calculate the square root of the right side: 11.191514643 Break this problem into two subproblems by setting (x + 1.5) equal to 11.191514643 and -11.191514643.Subproblem 1
x + 1.5 = 11.191514643 Simplifying x + 1.5 = 11.191514643 Reorder the terms: 1.5 + x = 11.191514643 Solving 1.5 + x = 11.191514643 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 = 11.191514643 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 11.191514643 + -1.5 x = 11.191514643 + -1.5 Combine like terms: 11.191514643 + -1.5 = 9.691514643 x = 9.691514643 Simplifying x = 9.691514643Subproblem 2
x + 1.5 = -11.191514643 Simplifying x + 1.5 = -11.191514643 Reorder the terms: 1.5 + x = -11.191514643 Solving 1.5 + x = -11.191514643 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 = -11.191514643 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -11.191514643 + -1.5 x = -11.191514643 + -1.5 Combine like terms: -11.191514643 + -1.5 = -12.691514643 x = -12.691514643 Simplifying x = -12.691514643Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.691514643, -12.691514643}Solution
x = {9.691514643, -12.691514643}
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