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Simplifying 0 = 2x2 + 4x + 40 Reorder the terms: 0 = 40 + 4x + 2x2 Solving 0 = 40 + 4x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -40 = -40 -40 + -4x + -2x2 = 40 + 4x + 2x2 + -40 + -4x + -2x2 Reorder the terms: -40 + -4x + -2x2 = 40 + -40 + 4x + -4x + 2x2 + -2x2 Combine like terms: 40 + -40 = 0 -40 + -4x + -2x2 = 0 + 4x + -4x + 2x2 + -2x2 -40 + -4x + -2x2 = 4x + -4x + 2x2 + -2x2 Combine like terms: 4x + -4x = 0 -40 + -4x + -2x2 = 0 + 2x2 + -2x2 -40 + -4x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -40 + -4x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(20 + 2x + x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(20 + 2x + x2)' equal to zero and attempt to solve: Simplifying 20 + 2x + x2 = 0 Solving 20 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + 2x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + 2x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 2x + x2 = 0 + -20 2x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 2x + x2 = -20 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -20 + 1 Reorder the terms: 1 + 2x + x2 = -20 + 1 Combine like terms: -20 + 1 = -19 1 + 2x + x2 = -19 Factor a perfect square on the left side: (x + 1)(x + 1) = -19 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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