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Simplifying 116 = 16x + -4x2 Solving 116 = 16x + -4x2 Solving for variable 'x'. Reorder the terms: 116 + -16x + 4x2 = 16x + -16x + -4x2 + 4x2 Combine like terms: 16x + -16x = 0 116 + -16x + 4x2 = 0 + -4x2 + 4x2 116 + -16x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 116 + -16x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(29 + -4x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(29 + -4x + x2)' equal to zero and attempt to solve: Simplifying 29 + -4x + x2 = 0 Solving 29 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-29' to each side of the equation. 29 + -4x + -29 + x2 = 0 + -29 Reorder the terms: 29 + -29 + -4x + x2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + -4x + x2 = 0 + -29 -4x + x2 = 0 + -29 Combine like terms: 0 + -29 = -29 -4x + x2 = -29 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 = -29 + 4 Reorder the terms: 4 + -4x + x2 = -29 + 4 Combine like terms: -29 + 4 = -25 4 + -4x + x2 = -25 Factor a perfect square on the left side: (x + -2)(x + -2) = -25 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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