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Simplifying 2(x * 2 + x + -1) + 4(x * 2x + 3) = 0 Reorder the terms for easier multiplication: 2(2x + x + -1) + 4(x * 2x + 3) = 0 Reorder the terms: 2(-1 + 2x + x) + 4(x * 2x + 3) = 0 Combine like terms: 2x + x = 3x 2(-1 + 3x) + 4(x * 2x + 3) = 0 (-1 * 2 + 3x * 2) + 4(x * 2x + 3) = 0 (-2 + 6x) + 4(x * 2x + 3) = 0 Reorder the terms for easier multiplication: -2 + 6x + 4(2x * x + 3) = 0 Multiply x * x -2 + 6x + 4(2x2 + 3) = 0 Reorder the terms: -2 + 6x + 4(3 + 2x2) = 0 -2 + 6x + (3 * 4 + 2x2 * 4) = 0 -2 + 6x + (12 + 8x2) = 0 Reorder the terms: -2 + 12 + 6x + 8x2 = 0 Combine like terms: -2 + 12 = 10 10 + 6x + 8x2 = 0 Solving 10 + 6x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 3x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 3x + 4x2)' equal to zero and attempt to solve: Simplifying 5 + 3x + 4x2 = 0 Solving 5 + 3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + 0.75x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 0.75x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 0.75x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 0.75x + x2 = 0 + -1.25 0.75x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 0.75x + x2 = -1.25 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = -1.25 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = -1.25 + 0.140625 Combine like terms: -1.25 + 0.140625 = -1.109375 0.140625 + 0.75x + x2 = -1.109375 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = -1.109375 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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