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Simplifying x = 2x2 + 4x + 10 Reorder the terms: x = 10 + 4x + 2x2 Solving x = 10 + 4x + 2x2 Solving for variable 'x'. Reorder the terms: -10 + x + -4x + -2x2 = 10 + 4x + 2x2 + -10 + -4x + -2x2 Combine like terms: x + -4x = -3x -10 + -3x + -2x2 = 10 + 4x + 2x2 + -10 + -4x + -2x2 Reorder the terms: -10 + -3x + -2x2 = 10 + -10 + 4x + -4x + 2x2 + -2x2 Combine like terms: 10 + -10 = 0 -10 + -3x + -2x2 = 0 + 4x + -4x + 2x2 + -2x2 -10 + -3x + -2x2 = 4x + -4x + 2x2 + -2x2 Combine like terms: 4x + -4x = 0 -10 + -3x + -2x2 = 0 + 2x2 + -2x2 -10 + -3x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -10 + -3x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(10 + 3x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(10 + 3x + 2x2)' equal to zero and attempt to solve: Simplifying 10 + 3x + 2x2 = 0 Solving 10 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 5 + 1.5x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + 1.5x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 1.5x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 1.5x + x2 = 0 + -5 1.5x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 1.5x + x2 = -5 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 = -5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -5 + 0.5625 Combine like terms: -5 + 0.5625 = -4.4375 0.5625 + 1.5x + x2 = -4.4375 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -4.4375 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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