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Simplifying 5(x + -1) + -2(x2 + 3x + 4) + -7(x + 7) = 0 Reorder the terms: 5(-1 + x) + -2(x2 + 3x + 4) + -7(x + 7) = 0 (-1 * 5 + x * 5) + -2(x2 + 3x + 4) + -7(x + 7) = 0 (-5 + 5x) + -2(x2 + 3x + 4) + -7(x + 7) = 0 Reorder the terms: -5 + 5x + -2(4 + 3x + x2) + -7(x + 7) = 0 -5 + 5x + (4 * -2 + 3x * -2 + x2 * -2) + -7(x + 7) = 0 -5 + 5x + (-8 + -6x + -2x2) + -7(x + 7) = 0 Reorder the terms: -5 + 5x + -8 + -6x + -2x2 + -7(7 + x) = 0 -5 + 5x + -8 + -6x + -2x2 + (7 * -7 + x * -7) = 0 -5 + 5x + -8 + -6x + -2x2 + (-49 + -7x) = 0 Reorder the terms: -5 + -8 + -49 + 5x + -6x + -7x + -2x2 = 0 Combine like terms: -5 + -8 = -13 -13 + -49 + 5x + -6x + -7x + -2x2 = 0 Combine like terms: -13 + -49 = -62 -62 + 5x + -6x + -7x + -2x2 = 0 Combine like terms: 5x + -6x = -1x -62 + -1x + -7x + -2x2 = 0 Combine like terms: -1x + -7x = -8x -62 + -8x + -2x2 = 0 Solving -62 + -8x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-2'. -2(31 + 4x + x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(31 + 4x + x2)' equal to zero and attempt to solve: Simplifying 31 + 4x + x2 = 0 Solving 31 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-31' to each side of the equation. 31 + 4x + -31 + x2 = 0 + -31 Reorder the terms: 31 + -31 + 4x + x2 = 0 + -31 Combine like terms: 31 + -31 = 0 0 + 4x + x2 = 0 + -31 4x + x2 = 0 + -31 Combine like terms: 0 + -31 = -31 4x + x2 = -31 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -31 + 4 Reorder the terms: 4 + 4x + x2 = -31 + 4 Combine like terms: -31 + 4 = -27 4 + 4x + x2 = -27 Factor a perfect square on the left side: (x + 2)(x + 2) = -27 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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