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Simplifying -3x2 + -14x + 2 = 2x + 7x2 + 11 Reorder the terms: 2 + -14x + -3x2 = 2x + 7x2 + 11 Reorder the terms: 2 + -14x + -3x2 = 11 + 2x + 7x2 Solving 2 + -14x + -3x2 = 11 + 2x + 7x2 Solving for variable 'x'. Reorder the terms: 2 + -11 + -14x + -2x + -3x2 + -7x2 = 11 + 2x + 7x2 + -11 + -2x + -7x2 Combine like terms: 2 + -11 = -9 -9 + -14x + -2x + -3x2 + -7x2 = 11 + 2x + 7x2 + -11 + -2x + -7x2 Combine like terms: -14x + -2x = -16x -9 + -16x + -3x2 + -7x2 = 11 + 2x + 7x2 + -11 + -2x + -7x2 Combine like terms: -3x2 + -7x2 = -10x2 -9 + -16x + -10x2 = 11 + 2x + 7x2 + -11 + -2x + -7x2 Reorder the terms: -9 + -16x + -10x2 = 11 + -11 + 2x + -2x + 7x2 + -7x2 Combine like terms: 11 + -11 = 0 -9 + -16x + -10x2 = 0 + 2x + -2x + 7x2 + -7x2 -9 + -16x + -10x2 = 2x + -2x + 7x2 + -7x2 Combine like terms: 2x + -2x = 0 -9 + -16x + -10x2 = 0 + 7x2 + -7x2 -9 + -16x + -10x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 -9 + -16x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(9 + 16x + 10x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + 16x + 10x2)' equal to zero and attempt to solve: Simplifying 9 + 16x + 10x2 = 0 Solving 9 + 16x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.9 + 1.6x + x2 = 0.0 Move the constant term to the right: Add '-0.9' to each side of the equation. 0.9 + 1.6x + -0.9 + x2 = 0.0 + -0.9 Reorder the terms: 0.9 + -0.9 + 1.6x + x2 = 0.0 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + 1.6x + x2 = 0.0 + -0.9 1.6x + x2 = 0.0 + -0.9 Combine like terms: 0.0 + -0.9 = -0.9 1.6x + x2 = -0.9 The x term is 1.6x. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6x + 0.64 + x2 = -0.9 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = -0.9 + 0.64 Combine like terms: -0.9 + 0.64 = -0.26 0.64 + 1.6x + x2 = -0.26 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = -0.26 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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