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Simplifying 4x + -1(16x2 + -1x + -15) = 49 + -1(6x2 + -13x + 2) Reorder the terms: 4x + -1(-15 + -1x + 16x2) = 49 + -1(6x2 + -13x + 2) 4x + (-15 * -1 + -1x * -1 + 16x2 * -1) = 49 + -1(6x2 + -13x + 2) 4x + (15 + 1x + -16x2) = 49 + -1(6x2 + -13x + 2) Reorder the terms: 15 + 4x + 1x + -16x2 = 49 + -1(6x2 + -13x + 2) Combine like terms: 4x + 1x = 5x 15 + 5x + -16x2 = 49 + -1(6x2 + -13x + 2) Reorder the terms: 15 + 5x + -16x2 = 49 + -1(2 + -13x + 6x2) 15 + 5x + -16x2 = 49 + (2 * -1 + -13x * -1 + 6x2 * -1) 15 + 5x + -16x2 = 49 + (-2 + 13x + -6x2) Combine like terms: 49 + -2 = 47 15 + 5x + -16x2 = 47 + 13x + -6x2 Solving 15 + 5x + -16x2 = 47 + 13x + -6x2 Solving for variable 'x'. Reorder the terms: 15 + -47 + 5x + -13x + -16x2 + 6x2 = 47 + 13x + -6x2 + -47 + -13x + 6x2 Combine like terms: 15 + -47 = -32 -32 + 5x + -13x + -16x2 + 6x2 = 47 + 13x + -6x2 + -47 + -13x + 6x2 Combine like terms: 5x + -13x = -8x -32 + -8x + -16x2 + 6x2 = 47 + 13x + -6x2 + -47 + -13x + 6x2 Combine like terms: -16x2 + 6x2 = -10x2 -32 + -8x + -10x2 = 47 + 13x + -6x2 + -47 + -13x + 6x2 Reorder the terms: -32 + -8x + -10x2 = 47 + -47 + 13x + -13x + -6x2 + 6x2 Combine like terms: 47 + -47 = 0 -32 + -8x + -10x2 = 0 + 13x + -13x + -6x2 + 6x2 -32 + -8x + -10x2 = 13x + -13x + -6x2 + 6x2 Combine like terms: 13x + -13x = 0 -32 + -8x + -10x2 = 0 + -6x2 + 6x2 -32 + -8x + -10x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 -32 + -8x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(16 + 4x + 5x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(16 + 4x + 5x2)' equal to zero and attempt to solve: Simplifying 16 + 4x + 5x2 = 0 Solving 16 + 4x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3.2 + 0.8x + x2 = 0 Move the constant term to the right: Add '-3.2' to each side of the equation. 3.2 + 0.8x + -3.2 + x2 = 0 + -3.2 Reorder the terms: 3.2 + -3.2 + 0.8x + x2 = 0 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + 0.8x + x2 = 0 + -3.2 0.8x + x2 = 0 + -3.2 Combine like terms: 0 + -3.2 = -3.2 0.8x + x2 = -3.2 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = -3.2 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = -3.2 + 0.16 Combine like terms: -3.2 + 0.16 = -3.04 0.16 + 0.8x + x2 = -3.04 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = -3.04 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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