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Simplifying (6x2 + -3x + 7) + (4x2 + 5x + -3) = 0 Reorder the terms: (7 + -3x + 6x2) + (4x2 + 5x + -3) = 0 Remove parenthesis around (7 + -3x + 6x2) 7 + -3x + 6x2 + (4x2 + 5x + -3) = 0 Reorder the terms: 7 + -3x + 6x2 + (-3 + 5x + 4x2) = 0 Remove parenthesis around (-3 + 5x + 4x2) 7 + -3x + 6x2 + -3 + 5x + 4x2 = 0 Reorder the terms: 7 + -3 + -3x + 5x + 6x2 + 4x2 = 0 Combine like terms: 7 + -3 = 4 4 + -3x + 5x + 6x2 + 4x2 = 0 Combine like terms: -3x + 5x = 2x 4 + 2x + 6x2 + 4x2 = 0 Combine like terms: 6x2 + 4x2 = 10x2 4 + 2x + 10x2 = 0 Solving 4 + 2x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + x + 5x2)' equal to zero and attempt to solve: Simplifying 2 + x + 5x2 = 0 Solving 2 + x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + 0.2x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + 0.2x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + 0.2x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 0.2x + x2 = 0 + -0.4 0.2x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 0.2x + x2 = -0.4 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.2x + 0.25 + x2 = -0.4 + 0.25 Reorder the terms: 0.25 + 0.2x + x2 = -0.4 + 0.25 Combine like terms: -0.4 + 0.25 = -0.15 0.25 + 0.2x + x2 = -0.15 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.15 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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