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Simplifying (-1x2 + 4x + -3) + (5x2 + 2x + 7) = 0 Reorder the terms: (-3 + 4x + -1x2) + (5x2 + 2x + 7) = 0 Remove parenthesis around (-3 + 4x + -1x2) -3 + 4x + -1x2 + (5x2 + 2x + 7) = 0 Reorder the terms: -3 + 4x + -1x2 + (7 + 2x + 5x2) = 0 Remove parenthesis around (7 + 2x + 5x2) -3 + 4x + -1x2 + 7 + 2x + 5x2 = 0 Reorder the terms: -3 + 7 + 4x + 2x + -1x2 + 5x2 = 0 Combine like terms: -3 + 7 = 4 4 + 4x + 2x + -1x2 + 5x2 = 0 Combine like terms: 4x + 2x = 6x 4 + 6x + -1x2 + 5x2 = 0 Combine like terms: -1x2 + 5x2 = 4x2 4 + 6x + 4x2 = 0 Solving 4 + 6x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + 3x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + 3x + 2x2)' equal to zero and attempt to solve: Simplifying 2 + 3x + 2x2 = 0 Solving 2 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1 + 1.5x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 1.5x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 1.5x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 1.5x + x2 = 0 + -1 1.5x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 1.5x + x2 = -1 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = -1 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -1 + 0.5625 Combine like terms: -1 + 0.5625 = -0.4375 0.5625 + 1.5x + x2 = -0.4375 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -0.4375 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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