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Simplifying 0 = 10x2 + 4x + 12 Reorder the terms: 0 = 12 + 4x + 10x2 Solving 0 = 12 + 4x + 10x2 Solving for variable 'x'. Combine like terms: 0 + -12 = -12 -12 + -4x + -10x2 = 12 + 4x + 10x2 + -12 + -4x + -10x2 Reorder the terms: -12 + -4x + -10x2 = 12 + -12 + 4x + -4x + 10x2 + -10x2 Combine like terms: 12 + -12 = 0 -12 + -4x + -10x2 = 0 + 4x + -4x + 10x2 + -10x2 -12 + -4x + -10x2 = 4x + -4x + 10x2 + -10x2 Combine like terms: 4x + -4x = 0 -12 + -4x + -10x2 = 0 + 10x2 + -10x2 -12 + -4x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 -12 + -4x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(6 + 2x + 5x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(6 + 2x + 5x2)' equal to zero and attempt to solve: Simplifying 6 + 2x + 5x2 = 0 Solving 6 + 2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.2 + 0.4x + x2 = 0 Move the constant term to the right: Add '-1.2' to each side of the equation. 1.2 + 0.4x + -1.2 + x2 = 0 + -1.2 Reorder the terms: 1.2 + -1.2 + 0.4x + x2 = 0 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + 0.4x + x2 = 0 + -1.2 0.4x + x2 = 0 + -1.2 Combine like terms: 0 + -1.2 = -1.2 0.4x + x2 = -1.2 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = -1.2 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = -1.2 + 0.04 Combine like terms: -1.2 + 0.04 = -1.16 0.04 + 0.4x + x2 = -1.16 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = -1.16 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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