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Simplifying 2x2 + -5x + -12 = 16x2 + 5x + 12 Reorder the terms: -12 + -5x + 2x2 = 16x2 + 5x + 12 Reorder the terms: -12 + -5x + 2x2 = 12 + 5x + 16x2 Solving -12 + -5x + 2x2 = 12 + 5x + 16x2 Solving for variable 'x'. Reorder the terms: -12 + -12 + -5x + -5x + 2x2 + -16x2 = 12 + 5x + 16x2 + -12 + -5x + -16x2 Combine like terms: -12 + -12 = -24 -24 + -5x + -5x + 2x2 + -16x2 = 12 + 5x + 16x2 + -12 + -5x + -16x2 Combine like terms: -5x + -5x = -10x -24 + -10x + 2x2 + -16x2 = 12 + 5x + 16x2 + -12 + -5x + -16x2 Combine like terms: 2x2 + -16x2 = -14x2 -24 + -10x + -14x2 = 12 + 5x + 16x2 + -12 + -5x + -16x2 Reorder the terms: -24 + -10x + -14x2 = 12 + -12 + 5x + -5x + 16x2 + -16x2 Combine like terms: 12 + -12 = 0 -24 + -10x + -14x2 = 0 + 5x + -5x + 16x2 + -16x2 -24 + -10x + -14x2 = 5x + -5x + 16x2 + -16x2 Combine like terms: 5x + -5x = 0 -24 + -10x + -14x2 = 0 + 16x2 + -16x2 -24 + -10x + -14x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -24 + -10x + -14x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(12 + 5x + 7x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(12 + 5x + 7x2)' equal to zero and attempt to solve: Simplifying 12 + 5x + 7x2 = 0 Solving 12 + 5x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1.714285714 + 0.7142857143x + x2 = 0 Move the constant term to the right: Add '-1.714285714' to each side of the equation. 1.714285714 + 0.7142857143x + -1.714285714 + x2 = 0 + -1.714285714 Reorder the terms: 1.714285714 + -1.714285714 + 0.7142857143x + x2 = 0 + -1.714285714 Combine like terms: 1.714285714 + -1.714285714 = 0.000000000 0.000000000 + 0.7142857143x + x2 = 0 + -1.714285714 0.7142857143x + x2 = 0 + -1.714285714 Combine like terms: 0 + -1.714285714 = -1.714285714 0.7142857143x + x2 = -1.714285714 The x term is 0.7142857143x. Take half its coefficient (0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. 0.7142857143x + 0.1275510204 + x2 = -1.714285714 + 0.1275510204 Reorder the terms: 0.1275510204 + 0.7142857143x + x2 = -1.714285714 + 0.1275510204 Combine like terms: -1.714285714 + 0.1275510204 = -1.5867346936 0.1275510204 + 0.7142857143x + x2 = -1.5867346936 Factor a perfect square on the left side: (x + 0.3571428572)(x + 0.3571428572) = -1.5867346936 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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